Weingarten functions for p = 13

Below are the values of the Weingarten function for permutation size p = 13. The input is given as a partition of p. You can also download them as a text file or as a python pickle file. \[\operatorname{Wg}([1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]) = \frac{n^{24} - 603 n^{22} + 152741 n^{20} - 21210567 n^{18} + 1769387586 n^{16} - 91536665094 n^{14} + 2936584675724 n^{12} - 57077713180764 n^{10} + 642097417997560 n^{8} - 3860971518054792 n^{6} + 10654648493155488 n^{4} - 10036770053460480 n^{2} + 892107907891200}{n^{3} \left(n^{34} - 681 n^{32} + 201348 n^{30} - 34091188 n^{28} + 3674787966 n^{26} - 265541411646 n^{24} + 13212831147540 n^{22} - 458682008560740 n^{20} + 11156814277906185 n^{18} - 189688724436717985 n^{16} + 2234929793350958304 n^{14} - 17964877694273373024 n^{12} + 96171169854071114752 n^{10} - 331100792818084806912 n^{8} + 698246093019750395904 n^{6} - 842376010740646477824 n^{4} + 527127365121343488000 n^{2} - 132158898894274560000\right)}\] \[\operatorname{Wg}([2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]) = \frac{- n^{22} + 581 n^{20} - 140509 n^{18} + 18410979 n^{16} - 1427211378 n^{14} + 67258303008 n^{12} - 1914984235028 n^{10} + 31924955452468 n^{8} - 294116685813464 n^{6} + 1348289963187264 n^{4} - 2488083675822720 n^{2} + 996961038796800}{n^{2} \left(n^{34} - 681 n^{32} + 201348 n^{30} - 34091188 n^{28} + 3674787966 n^{26} - 265541411646 n^{24} + 13212831147540 n^{22} - 458682008560740 n^{20} + 11156814277906185 n^{18} - 189688724436717985 n^{16} + 2234929793350958304 n^{14} - 17964877694273373024 n^{12} + 96171169854071114752 n^{10} - 331100792818084806912 n^{8} + 698246093019750395904 n^{6} - 842376010740646477824 n^{4} + 527127365121343488000 n^{2} - 132158898894274560000\right)}\] \[\operatorname{Wg}([3, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]) = \frac{2 n^{22} - 1112 n^{20} + 254508 n^{18} - 31106928 n^{16} + 2207123826 n^{14} - 92872767336 n^{12} + 2286614338936 n^{10} - 31634612016736 n^{8} + 228425595897048 n^{6} - 742414983393888 n^{4} + 821800819514880 n^{2} - 81100718899200}{n^{3} \left(n^{34} - 681 n^{32} + 201348 n^{30} - 34091188 n^{28} + 3674787966 n^{26} - 265541411646 n^{24} + 13212831147540 n^{22} - 458682008560740 n^{20} + 11156814277906185 n^{18} - 189688724436717985 n^{16} + 2234929793350958304 n^{14} - 17964877694273373024 n^{12} + 96171169854071114752 n^{10} - 331100792818084806912 n^{8} + 698246093019750395904 n^{6} - 842376010740646477824 n^{4} + 527127365121343488000 n^{2} - 132158898894274560000\right)}\] \[\operatorname{Wg}([2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1]) = \frac{n^{22} - 553 n^{20} + 125865 n^{18} - 15302895 n^{16} + 1081209414 n^{14} - 45397176672 n^{12} + 1118487357908 n^{10} - 15519866221364 n^{8} + 112544951199432 n^{6} - 372071044283616 n^{4} + 417731679290880 n^{2} - 82112370278400}{n^{3} \left(n^{34} - 681 n^{32} + 201348 n^{30} - 34091188 n^{28} + 3674787966 n^{26} - 265541411646 n^{24} + 13212831147540 n^{22} - 458682008560740 n^{20} + 11156814277906185 n^{18} - 189688724436717985 n^{16} + 2234929793350958304 n^{14} - 17964877694273373024 n^{12} + 96171169854071114752 n^{10} - 331100792818084806912 n^{8} + 698246093019750395904 n^{6} - 842376010740646477824 n^{4} + 527127365121343488000 n^{2} - 132158898894274560000\right)}\] \[\operatorname{Wg}([4, 1, 1, 1, 1, 1, 1, 1, 1, 1]) = \frac{- 5 n^{20} + 2651 n^{18} - 571503 n^{16} + 64729893 n^{14} - 4164383868 n^{12} + 154335413112 n^{10} - 3221529888820 n^{8} + 35980777572988 n^{6} - 195416494298064 n^{4} + 415436653213056 n^{2} - 191282135869440}{n^{2} \left(n^{34} - 681 n^{32} + 201348 n^{30} - 34091188 n^{28} + 3674787966 n^{26} - 265541411646 n^{24} + 13212831147540 n^{22} - 458682008560740 n^{20} + 11156814277906185 n^{18} - 189688724436717985 n^{16} + 2234929793350958304 n^{14} - 17964877694273373024 n^{12} + 96171169854071114752 n^{10} - 331100792818084806912 n^{8} + 698246093019750395904 n^{6} - 842376010740646477824 n^{4} + 527127365121343488000 n^{2} - 132158898894274560000\right)}\] \[\operatorname{Wg}([3, 2, 1, 1, 1, 1, 1, 1, 1, 1]) = \frac{- 2 n^{20} + 1038 n^{18} - 218342 n^{16} + 24060242 n^{14} - 1503595400 n^{12} + 54202894544 n^{10} - 1106892161496 n^{8} + 12178908829784 n^{6} - 65042881145280 n^{4} + 137719854456192 n^{2} - 59142710753280}{n^{2} \left(n^{34} - 681 n^{32} + 201348 n^{30} - 34091188 n^{28} + 3674787966 n^{26} - 265541411646 n^{24} + 13212831147540 n^{22} - 458682008560740 n^{20} + 11156814277906185 n^{18} - 189688724436717985 n^{16} + 2234929793350958304 n^{14} - 17964877694273373024 n^{12} + 96171169854071114752 n^{10} - 331100792818084806912 n^{8} + 698246093019750395904 n^{6} - 842376010740646477824 n^{4} + 527127365121343488000 n^{2} - 132158898894274560000\right)}\] \[\operatorname{Wg}([5, 1, 1, 1, 1, 1, 1, 1, 1]) = \frac{14 n^{20} - 7042 n^{18} + 1420762 n^{16} - 147897022 n^{14} + 8534144248 n^{12} - 274465127440 n^{10} + 4756479186872 n^{8} - 41553294299496 n^{6} + 160162706428704 n^{4} - 207783464716800 n^{2} + 27145978675200}{n^{3} \left(n^{34} - 681 n^{32} + 201348 n^{30} - 34091188 n^{28} + 3674787966 n^{26} - 265541411646 n^{24} + 13212831147540 n^{22} - 458682008560740 n^{20} + 11156814277906185 n^{18} - 189688724436717985 n^{16} + 2234929793350958304 n^{14} - 17964877694273373024 n^{12} + 96171169854071114752 n^{10} - 331100792818084806912 n^{8} + 698246093019750395904 n^{6} - 842376010740646477824 n^{4} + 527127365121343488000 n^{2} - 132158898894274560000\right)}\] \[\operatorname{Wg}([2, 2, 2, 1, 1, 1, 1, 1, 1, 1]) = \frac{- n^{20} + 519 n^{18} - 109549 n^{16} + 12181279 n^{14} - 774334438 n^{12} + 28658931550 n^{10} - 604264622088 n^{8} + 6827895761752 n^{6} - 37452489143424 n^{4} + 88655287248000 n^{2} - 102662496921600}{n^{2} \left(n^{34} - 681 n^{32} + 201348 n^{30} - 34091188 n^{28} + 3674787966 n^{26} - 265541411646 n^{24} + 13212831147540 n^{22} - 458682008560740 n^{20} + 11156814277906185 n^{18} - 189688724436717985 n^{16} + 2234929793350958304 n^{14} - 17964877694273373024 n^{12} + 96171169854071114752 n^{10} - 331100792818084806912 n^{8} + 698246093019750395904 n^{6} - 842376010740646477824 n^{4} + 527127365121343488000 n^{2} - 132158898894274560000\right)}\] \[\operatorname{Wg}([4, 2, 1, 1, 1, 1, 1, 1, 1]) = \frac{5 n^{20} - 2413 n^{18} + 463003 n^{16} - 45378673 n^{14} + 2440396288 n^{12} - 72644037430 n^{10} + 1168483154900 n^{8} - 9617554081824 n^{6} + 35762102656704 n^{4} - 45094214799360 n^{2} + 13741597900800}{n^{3} \left(n^{34} - 681 n^{32} + 201348 n^{30} - 34091188 n^{28} + 3674787966 n^{26} - 265541411646 n^{24} + 13212831147540 n^{22} - 458682008560740 n^{20} + 11156814277906185 n^{18} - 189688724436717985 n^{16} + 2234929793350958304 n^{14} - 17964877694273373024 n^{12} + 96171169854071114752 n^{10} - 331100792818084806912 n^{8} + 698246093019750395904 n^{6} - 842376010740646477824 n^{4} + 527127365121343488000 n^{2} - 132158898894274560000\right)}\] \[\operatorname{Wg}([3, 3, 1, 1, 1, 1, 1, 1, 1]) = \frac{4 n^{20} - 1880 n^{18} + 348050 n^{16} - 32479670 n^{14} + 1633430006 n^{12} - 44540849390 n^{10} + 648283203292 n^{8} - 4840353981660 n^{6} + 15525876206448 n^{4} - 17413464326400 n^{2} - 42152140800}{n^{3} \left(n^{34} - 681 n^{32} + 201348 n^{30} - 34091188 n^{28} + 3674787966 n^{26} - 265541411646 n^{24} + 13212831147540 n^{22} - 458682008560740 n^{20} + 11156814277906185 n^{18} - 189688724436717985 n^{16} + 2234929793350958304 n^{14} - 17964877694273373024 n^{12} + 96171169854071114752 n^{10} - 331100792818084806912 n^{8} + 698246093019750395904 n^{6} - 842376010740646477824 n^{4} + 527127365121343488000 n^{2} - 132158898894274560000\right)}\] \[\operatorname{Wg}([6, 1, 1, 1, 1, 1, 1, 1]) = \frac{- 42 n^{18} + 19866 n^{16} - 3710406 n^{14} + 350226786 n^{12} - 17826435984 n^{10} + 487545614220 n^{8} - 6845759813256 n^{6} + 45094505557248 n^{4} - 112316193827712 n^{2} + 59212964321280}{n^{2} \left(n^{34} - 681 n^{32} + 201348 n^{30} - 34091188 n^{28} + 3674787966 n^{26} - 265541411646 n^{24} + 13212831147540 n^{22} - 458682008560740 n^{20} + 11156814277906185 n^{18} - 189688724436717985 n^{16} + 2234929793350958304 n^{14} - 17964877694273373024 n^{12} + 96171169854071114752 n^{10} - 331100792818084806912 n^{8} + 698246093019750395904 n^{6} - 842376010740646477824 n^{4} + 527127365121343488000 n^{2} - 132158898894274560000\right)}\] \[\operatorname{Wg}([3, 2, 2, 1, 1, 1, 1, 1, 1]) = \frac{2 n^{18} - 950 n^{16} + 180422 n^{14} - 17728190 n^{12} + 978937520 n^{10} - 30970574780 n^{8} + 543034830936 n^{6} - 4688714558880 n^{4} + 15363763499520 n^{2} - 3877996953600}{n^{3} \left(n^{32} - 680 n^{30} + 200668 n^{28} - 33890520 n^{26} + 3640897446 n^{24} - 261900514200 n^{22} + 12950930633340 n^{20} - 445731077927400 n^{18} + 10711083199978785 n^{16} - 178977641236739200 n^{14} + 2055952152114219104 n^{12} - 15908925542159153920 n^{10} + 80262244311911960832 n^{8} - 250838548506172846080 n^{6} + 447407544513577549824 n^{4} - 394968466227068928000 n^{2} + 132158898894274560000\right)}\] \[\operatorname{Wg}([5, 2, 1, 1, 1, 1, 1, 1]) = \frac{- 14 n^{18} + 6214 n^{16} - 1071754 n^{14} + 91525054 n^{12} - 4109687320 n^{10} + 96353508820 n^{8} - 1125234244712 n^{6} + 5941019666112 n^{4} - 13481199100800 n^{2} + 12682913126400}{n^{2} \left(n^{34} - 681 n^{32} + 201348 n^{30} - 34091188 n^{28} + 3674787966 n^{26} - 265541411646 n^{24} + 13212831147540 n^{22} - 458682008560740 n^{20} + 11156814277906185 n^{18} - 189688724436717985 n^{16} + 2234929793350958304 n^{14} - 17964877694273373024 n^{12} + 96171169854071114752 n^{10} - 331100792818084806912 n^{8} + 698246093019750395904 n^{6} - 842376010740646477824 n^{4} + 527127365121343488000 n^{2} - 132158898894274560000\right)}\] \[\operatorname{Wg}([4, 3, 1, 1, 1, 1, 1, 1]) = \frac{- 10 n^{16} + 4138 n^{14} - 640090 n^{12} + 45514258 n^{10} - 1438147420 n^{8} + 13256749300 n^{6} + 158944715280 n^{4} - 2801573940096 n^{2} + 8473045616640}{n^{2} \left(n^{32} - 680 n^{30} + 200668 n^{28} - 33890520 n^{26} + 3640897446 n^{24} - 261900514200 n^{22} + 12950930633340 n^{20} - 445731077927400 n^{18} + 10711083199978785 n^{16} - 178977641236739200 n^{14} + 2055952152114219104 n^{12} - 15908925542159153920 n^{10} + 80262244311911960832 n^{8} - 250838548506172846080 n^{6} + 447407544513577549824 n^{4} - 394968466227068928000 n^{2} + 132158898894274560000\right)}\] \[\operatorname{Wg}([7, 1, 1, 1, 1, 1, 1]) = \frac{132 n^{18} - 57882 n^{16} + 9829182 n^{14} - 822296442 n^{12} + 35887652130 n^{10} - 807492581940 n^{8} + 8869649312436 n^{6} - 42151328649936 n^{4} + 66279408433920 n^{2} - 11676143001600}{n^{3} \left(n^{34} - 681 n^{32} + 201348 n^{30} - 34091188 n^{28} + 3674787966 n^{26} - 265541411646 n^{24} + 13212831147540 n^{22} - 458682008560740 n^{20} + 11156814277906185 n^{18} - 189688724436717985 n^{16} + 2234929793350958304 n^{14} - 17964877694273373024 n^{12} + 96171169854071114752 n^{10} - 331100792818084806912 n^{8} + 698246093019750395904 n^{6} - 842376010740646477824 n^{4} + 527127365121343488000 n^{2} - 132158898894274560000\right)}\] \[\operatorname{Wg}([2, 2, 2, 2, 1, 1, 1, 1, 1]) = \frac{n^{20} - 479 n^{18} + 92409 n^{16} - 9286259 n^{14} + 524161498 n^{12} - 16599653010 n^{10} + 275825074648 n^{8} - 2105678347112 n^{6} + 7255819837344 n^{4} - 28656787530240 n^{2} + 35576406835200}{n^{3} \left(n^{34} - 681 n^{32} + 201348 n^{30} - 34091188 n^{28} + 3674787966 n^{26} - 265541411646 n^{24} + 13212831147540 n^{22} - 458682008560740 n^{20} + 11156814277906185 n^{18} - 189688724436717985 n^{16} + 2234929793350958304 n^{14} - 17964877694273373024 n^{12} + 96171169854071114752 n^{10} - 331100792818084806912 n^{8} + 698246093019750395904 n^{6} - 842376010740646477824 n^{4} + 527127365121343488000 n^{2} - 132158898894274560000\right)}\] \[\operatorname{Wg}([4, 2, 2, 1, 1, 1, 1, 1]) = \frac{- 5 n^{18} + 2145 n^{16} - 361155 n^{14} + 30983825 n^{12} - 1488266920 n^{10} + 41518300530 n^{8} - 653850859140 n^{6} + 5181403594000 n^{4} - 17357336273280 n^{2} + 25119224064000}{n^{2} \left(n^{34} - 681 n^{32} + 201348 n^{30} - 34091188 n^{28} + 3674787966 n^{26} - 265541411646 n^{24} + 13212831147540 n^{22} - 458682008560740 n^{20} + 11156814277906185 n^{18} - 189688724436717985 n^{16} + 2234929793350958304 n^{14} - 17964877694273373024 n^{12} + 96171169854071114752 n^{10} - 331100792818084806912 n^{8} + 698246093019750395904 n^{6} - 842376010740646477824 n^{4} + 527127365121343488000 n^{2} - 132158898894274560000\right)}\] \[\operatorname{Wg}([3, 3, 2, 1, 1, 1, 1, 1]) = \frac{- 4 n^{18} + 1672 n^{16} - 274652 n^{14} + 23340972 n^{12} - 1159499488 n^{10} + 35739405980 n^{8} - 643805439632 n^{6} + 5514730233216 n^{4} - 16763955969024 n^{2} + 5693677608960}{n^{2} \left(n^{34} - 681 n^{32} + 201348 n^{30} - 34091188 n^{28} + 3674787966 n^{26} - 265541411646 n^{24} + 13212831147540 n^{22} - 458682008560740 n^{20} + 11156814277906185 n^{18} - 189688724436717985 n^{16} + 2234929793350958304 n^{14} - 17964877694273373024 n^{12} + 96171169854071114752 n^{10} - 331100792818084806912 n^{8} + 698246093019750395904 n^{6} - 842376010740646477824 n^{4} + 527127365121343488000 n^{2} - 132158898894274560000\right)}\] \[\operatorname{Wg}([6, 2, 1, 1, 1, 1, 1]) = \frac{42 n^{16} - 16200 n^{14} + 2305992 n^{12} - 149744760 n^{10} + 4447131570 n^{8} - 52972180320 n^{6} + 155493223596 n^{4} + 180340739280 n^{2} + 123821913600}{n^{3} \left(n^{32} - 665 n^{30} + 190708 n^{28} - 31039860 n^{26} + 3178150206 n^{24} - 214691008350 n^{22} + 9777775013940 n^{20} - 302237608337700 n^{18} + 6321012544502985 n^{16} - 88552523724670225 n^{14} + 818089413756234704 n^{12} - 4875447074173617760 n^{10} + 18164016667293230592 n^{8} - 40476526141393117440 n^{6} + 50621674757460516864 n^{4} - 32429214621278208000 n^{2} + 8259931180892160000\right)}\] \[\operatorname{Wg}([5, 3, 1, 1, 1, 1, 1]) = \frac{28 n^{18} - 9933 n^{16} + 1204343 n^{14} - 52162453 n^{12} - 221107005 n^{10} + 67702994590 n^{8} - 1455995321466 n^{6} + 10679189320296 n^{4} - 22716081763200 n^{2} + 5205789388800}{n^{3} \left(n^{34} - 681 n^{32} + 201348 n^{30} - 34091188 n^{28} + 3674787966 n^{26} - 265541411646 n^{24} + 13212831147540 n^{22} - 458682008560740 n^{20} + 11156814277906185 n^{18} - 189688724436717985 n^{16} + 2234929793350958304 n^{14} - 17964877694273373024 n^{12} + 96171169854071114752 n^{10} - 331100792818084806912 n^{8} + 698246093019750395904 n^{6} - 842376010740646477824 n^{4} + 527127365121343488000 n^{2} - 132158898894274560000\right)}\] \[\operatorname{Wg}([4, 4, 1, 1, 1, 1, 1]) = \frac{25 n^{18} - 8375 n^{16} + 881045 n^{14} - 17990855 n^{12} - 2159571730 n^{10} + 124552675330 n^{8} - 2213828405120 n^{6} + 14301081621600 n^{4} - 27742693086720 n^{2} + 3203562700800}{n^{3} \left(n^{34} - 681 n^{32} + 201348 n^{30} - 34091188 n^{28} + 3674787966 n^{26} - 265541411646 n^{24} + 13212831147540 n^{22} - 458682008560740 n^{20} + 11156814277906185 n^{18} - 189688724436717985 n^{16} + 2234929793350958304 n^{14} - 17964877694273373024 n^{12} + 96171169854071114752 n^{10} - 331100792818084806912 n^{8} + 698246093019750395904 n^{6} - 842376010740646477824 n^{4} + 527127365121343488000 n^{2} - 132158898894274560000\right)}\] \[\operatorname{Wg}([8, 1, 1, 1, 1, 1]) = \frac{- 429 n^{14} + 170170 n^{12} - 25415819 n^{10} + 1799903820 n^{8} - 63149339110 n^{6} + 1067011139480 n^{4} - 7932769608192 n^{2} + 19194920110080}{n^{2} \left(n^{32} - 680 n^{30} + 200668 n^{28} - 33890520 n^{26} + 3640897446 n^{24} - 261900514200 n^{22} + 12950930633340 n^{20} - 445731077927400 n^{18} + 10711083199978785 n^{16} - 178977641236739200 n^{14} + 2055952152114219104 n^{12} - 15908925542159153920 n^{10} + 80262244311911960832 n^{8} - 250838548506172846080 n^{6} + 447407544513577549824 n^{4} - 394968466227068928000 n^{2} + 132158898894274560000\right)}\] \[\operatorname{Wg}([3, 2, 2, 2, 1, 1, 1, 1]) = \frac{- 2 n^{18} + 854 n^{16} - 145618 n^{14} + 12853998 n^{12} - 625935404 n^{10} + 15865948852 n^{8} - 159822451960 n^{6} - 178350451584 n^{4} + 8829103584384 n^{2} - 16725850859520}{n^{2} \left(n^{34} - 681 n^{32} + 201348 n^{30} - 34091188 n^{28} + 3674787966 n^{26} - 265541411646 n^{24} + 13212831147540 n^{22} - 458682008560740 n^{20} + 11156814277906185 n^{18} - 189688724436717985 n^{16} + 2234929793350958304 n^{14} - 17964877694273373024 n^{12} + 96171169854071114752 n^{10} - 331100792818084806912 n^{8} + 698246093019750395904 n^{6} - 842376010740646477824 n^{4} + 527127365121343488000 n^{2} - 132158898894274560000\right)}\] \[\operatorname{Wg}([5, 2, 2, 1, 1, 1, 1]) = \frac{14 n^{16} - 5288 n^{14} + 766490 n^{12} - 55766204 n^{10} + 2265871028 n^{8} - 52430106008 n^{6} + 622686113568 n^{4} - 3531961152000 n^{2} + 7081559654400}{n^{3} \left(n^{32} - 680 n^{30} + 200668 n^{28} - 33890520 n^{26} + 3640897446 n^{24} - 261900514200 n^{22} + 12950930633340 n^{20} - 445731077927400 n^{18} + 10711083199978785 n^{16} - 178977641236739200 n^{14} + 2055952152114219104 n^{12} - 15908925542159153920 n^{10} + 80262244311911960832 n^{8} - 250838548506172846080 n^{6} + 447407544513577549824 n^{4} - 394968466227068928000 n^{2} + 132158898894274560000\right)}\] \[\operatorname{Wg}([4, 3, 2, 1, 1, 1, 1]) = \frac{10 n^{16} - 2522 n^{14} + 222198 n^{12} - 11697226 n^{10} + 444815288 n^{8} - 8964972132 n^{6} + 73825759440 n^{4} - 172769310720 n^{2} + 24448241664}{n^{3} \left(n^{32} - 581 n^{30} + 143248 n^{28} - 19766388 n^{26} + 1698149166 n^{24} - 95726495046 n^{22} + 3640181642940 n^{20} - 94663844266740 n^{18} + 1690429851232185 n^{16} - 20645739313499485 n^{14} + 170355862001009804 n^{12} - 929291494172392624 n^{10} + 3242020436831852352 n^{8} - 6898749134899571712 n^{6} + 8371179529793224704 n^{4} - 5258057761324007424 n^{2} + 1321588988942745600\right)}\] \[\operatorname{Wg}([7, 2, 1, 1, 1, 1]) = \frac{- 132 n^{12} + 32428 n^{10} - 2455772 n^{8} + 75479844 n^{6} - 1054152880 n^{4} + 4886792768 n^{2} - 9094880256}{n^{2} \left(n^{30} - 572 n^{28} + 138100 n^{26} - 18523488 n^{24} + 1531437774 n^{22} - 81943555080 n^{20} + 2902689647220 n^{18} - 68539637441760 n^{16} + 1073573114256345 n^{14} - 10983581285192380 n^{12} + 71503630434278384 n^{10} - 285758820263887168 n^{8} + 670191054456867840 n^{6} - 867029644787761152 n^{4} + 567912726703374336 n^{2} - 146843220993638400\right)}\] \[\operatorname{Wg}([3, 3, 3, 1, 1, 1, 1]) = \frac{8 n^{18} - 2760 n^{16} + 382528 n^{14} - 32191160 n^{12} + 2025617088 n^{10} - 82139146240 n^{8} + 1612319135448 n^{6} - 12567411231840 n^{4} + 29603255459328 n^{2} - 6238516838400}{n^{3} \left(n^{34} - 681 n^{32} + 201348 n^{30} - 34091188 n^{28} + 3674787966 n^{26} - 265541411646 n^{24} + 13212831147540 n^{22} - 458682008560740 n^{20} + 11156814277906185 n^{18} - 189688724436717985 n^{16} + 2234929793350958304 n^{14} - 17964877694273373024 n^{12} + 96171169854071114752 n^{10} - 331100792818084806912 n^{8} + 698246093019750395904 n^{6} - 842376010740646477824 n^{4} + 527127365121343488000 n^{2} - 132158898894274560000\right)}\] \[\operatorname{Wg}([6, 3, 1, 1, 1, 1]) = \frac{- 84 n^{16} + 24324 n^{14} - 2014044 n^{12} + 6294084 n^{10} + 5255225760 n^{8} - 187650233400 n^{6} + 2242345953408 n^{4} - 9537662913408 n^{2} + 11587541391360}{n^{2} \left(n^{34} - 681 n^{32} + 201348 n^{30} - 34091188 n^{28} + 3674787966 n^{26} - 265541411646 n^{24} + 13212831147540 n^{22} - 458682008560740 n^{20} + 11156814277906185 n^{18} - 189688724436717985 n^{16} + 2234929793350958304 n^{14} - 17964877694273373024 n^{12} + 96171169854071114752 n^{10} - 331100792818084806912 n^{8} + 698246093019750395904 n^{6} - 842376010740646477824 n^{4} + 527127365121343488000 n^{2} - 132158898894274560000\right)}\] \[\operatorname{Wg}([5, 4, 1, 1, 1, 1]) = \frac{- 70 n^{14} + 17164 n^{12} - 574378 n^{10} - 137797688 n^{8} + 12729442796 n^{6} - 376138273616 n^{4} + 4111396743552 n^{2} - 13080596981760}{n^{2} \left(n^{32} - 680 n^{30} + 200668 n^{28} - 33890520 n^{26} + 3640897446 n^{24} - 261900514200 n^{22} + 12950930633340 n^{20} - 445731077927400 n^{18} + 10711083199978785 n^{16} - 178977641236739200 n^{14} + 2055952152114219104 n^{12} - 15908925542159153920 n^{10} + 80262244311911960832 n^{8} - 250838548506172846080 n^{6} + 447407544513577549824 n^{4} - 394968466227068928000 n^{2} + 132158898894274560000\right)}\] \[\operatorname{Wg}([9, 1, 1, 1, 1]) = \frac{1430 n^{12} - 474188 n^{10} + 54889978 n^{8} - 2641357576 n^{6} + 48842399892 n^{4} - 251376489936 n^{2} + 171243072000}{n^{3} \left(n^{30} - 664 n^{28} + 190044 n^{26} - 30849816 n^{24} + 3147300390 n^{22} - 211543707960 n^{20} + 9566231305980 n^{18} - 292671377031720 n^{16} + 6028341167471265 n^{14} - 82524182557198960 n^{12} + 735565231199035744 n^{10} - 4139881842974582016 n^{8} + 14024134824318648576 n^{6} - 26452391317074468864 n^{4} + 24169283440386048000 n^{2} - 8259931180892160000\right)}\] \[\operatorname{Wg}([2, 2, 2, 2, 2, 1, 1, 1]) = \frac{- n^{18} + 433 n^{16} - 75401 n^{14} + 6770607 n^{12} - 331340122 n^{10} + 8732408732 n^{8} - 125810469464 n^{6} + 1190100224448 n^{4} - 12656114934912 n^{2} + 32132586055680}{n^{2} \left(n^{34} - 681 n^{32} + 201348 n^{30} - 34091188 n^{28} + 3674787966 n^{26} - 265541411646 n^{24} + 13212831147540 n^{22} - 458682008560740 n^{20} + 11156814277906185 n^{18} - 189688724436717985 n^{16} + 2234929793350958304 n^{14} - 17964877694273373024 n^{12} + 96171169854071114752 n^{10} - 331100792818084806912 n^{8} + 698246093019750395904 n^{6} - 842376010740646477824 n^{4} + 527127365121343488000 n^{2} - 132158898894274560000\right)}\] \[\operatorname{Wg}([4, 2, 2, 2, 1, 1, 1]) = \frac{5 n^{18} - 1847 n^{16} + 271963 n^{14} - 20797857 n^{12} + 850883444 n^{10} - 15912958780 n^{8} + 84752457088 n^{6} + 396785083584 n^{4} + 2589575270400 n^{2} - 7165863936000}{n^{3} \left(n^{34} - 681 n^{32} + 201348 n^{30} - 34091188 n^{28} + 3674787966 n^{26} - 265541411646 n^{24} + 13212831147540 n^{22} - 458682008560740 n^{20} + 11156814277906185 n^{18} - 189688724436717985 n^{16} + 2234929793350958304 n^{14} - 17964877694273373024 n^{12} + 96171169854071114752 n^{10} - 331100792818084806912 n^{8} + 698246093019750395904 n^{6} - 842376010740646477824 n^{4} + 527127365121343488000 n^{2} - 132158898894274560000\right)}\] \[\operatorname{Wg}([3, 3, 2, 2, 1, 1, 1]) = \frac{4 n^{16} - 1376 n^{14} + 188406 n^{12} - 13351534 n^{10} + 451500506 n^{8} - 1853246634 n^{6} - 153787123116 n^{4} + 990341323344 n^{2} - 424155916800}{n^{3} \left(n^{32} - 665 n^{30} + 190708 n^{28} - 31039860 n^{26} + 3178150206 n^{24} - 214691008350 n^{22} + 9777775013940 n^{20} - 302237608337700 n^{18} + 6321012544502985 n^{16} - 88552523724670225 n^{14} + 818089413756234704 n^{12} - 4875447074173617760 n^{10} + 18164016667293230592 n^{8} - 40476526141393117440 n^{6} + 50621674757460516864 n^{4} - 32429214621278208000 n^{2} + 8259931180892160000\right)}\] \[\operatorname{Wg}([6, 2, 2, 1, 1, 1]) = \frac{- 42 n^{16} + 13626 n^{14} - 1676514 n^{12} + 104347662 n^{10} - 3526479756 n^{8} + 50336284368 n^{6} + 27628129152 n^{4} - 3778719296256 n^{2} + 5759095541760}{n^{2} \left(n^{34} - 681 n^{32} + 201348 n^{30} - 34091188 n^{28} + 3674787966 n^{26} - 265541411646 n^{24} + 13212831147540 n^{22} - 458682008560740 n^{20} + 11156814277906185 n^{18} - 189688724436717985 n^{16} + 2234929793350958304 n^{14} - 17964877694273373024 n^{12} + 96171169854071114752 n^{10} - 331100792818084806912 n^{8} + 698246093019750395904 n^{6} - 842376010740646477824 n^{4} + 527127365121343488000 n^{2} - 132158898894274560000\right)}\] \[\operatorname{Wg}([5, 3, 2, 1, 1, 1]) = \frac{- 28 n^{16} + 7857 n^{14} - 815789 n^{12} + 50193937 n^{10} - 2483439843 n^{8} + 72311719130 n^{6} - 827244503760 n^{4} + 2576097137376 n^{2} + 2291103429120}{n^{2} \left(n^{34} - 681 n^{32} + 201348 n^{30} - 34091188 n^{28} + 3674787966 n^{26} - 265541411646 n^{24} + 13212831147540 n^{22} - 458682008560740 n^{20} + 11156814277906185 n^{18} - 189688724436717985 n^{16} + 2234929793350958304 n^{14} - 17964877694273373024 n^{12} + 96171169854071114752 n^{10} - 331100792818084806912 n^{8} + 698246093019750395904 n^{6} - 842376010740646477824 n^{4} + 527127365121343488000 n^{2} - 132158898894274560000\right)}\] \[\operatorname{Wg}([4, 4, 2, 1, 1, 1]) = \frac{- 25 n^{16} + 6545 n^{14} - 607661 n^{12} + 36766451 n^{10} - 2339494598 n^{8} + 91057228328 n^{6} - 1455140107936 n^{4} + 7559864731776 n^{2} - 10303312250880}{n^{2} \left(n^{34} - 681 n^{32} + 201348 n^{30} - 34091188 n^{28} + 3674787966 n^{26} - 265541411646 n^{24} + 13212831147540 n^{22} - 458682008560740 n^{20} + 11156814277906185 n^{18} - 189688724436717985 n^{16} + 2234929793350958304 n^{14} - 17964877694273373024 n^{12} + 96171169854071114752 n^{10} - 331100792818084806912 n^{8} + 698246093019750395904 n^{6} - 842376010740646477824 n^{4} + 527127365121343488000 n^{2} - 132158898894274560000\right)}\] \[\operatorname{Wg}([8, 2, 1, 1, 1]) = \frac{429 n^{14} - 128700 n^{12} + 13843401 n^{10} - 711818250 n^{8} + 21180375216 n^{6} - 368460549600 n^{4} + 2679886370304 n^{2} - 4383822643200}{n^{3} \left(n^{32} - 680 n^{30} + 200668 n^{28} - 33890520 n^{26} + 3640897446 n^{24} - 261900514200 n^{22} + 12950930633340 n^{20} - 445731077927400 n^{18} + 10711083199978785 n^{16} - 178977641236739200 n^{14} + 2055952152114219104 n^{12} - 15908925542159153920 n^{10} + 80262244311911960832 n^{8} - 250838548506172846080 n^{6} + 447407544513577549824 n^{4} - 394968466227068928000 n^{2} + 132158898894274560000\right)}\] \[\operatorname{Wg}([4, 3, 3, 1, 1, 1]) = \frac{- 20 n^{14} + 4888 n^{12} - 523422 n^{10} + 55529594 n^{8} - 4329281566 n^{6} + 131029780998 n^{4} - 882554742792 n^{2} + 1166782605120}{n^{2} \left(n^{32} - 665 n^{30} + 190708 n^{28} - 31039860 n^{26} + 3178150206 n^{24} - 214691008350 n^{22} + 9777775013940 n^{20} - 302237608337700 n^{18} + 6321012544502985 n^{16} - 88552523724670225 n^{14} + 818089413756234704 n^{12} - 4875447074173617760 n^{10} + 18164016667293230592 n^{8} - 40476526141393117440 n^{6} + 50621674757460516864 n^{4} - 32429214621278208000 n^{2} + 8259931180892160000\right)}\] \[\operatorname{Wg}([7, 3, 1, 1, 1]) = \frac{264 n^{16} - 57618 n^{14} + 2283468 n^{12} + 169629504 n^{10} - 10648690668 n^{8} + 122139159186 n^{6} + 44755154136 n^{4} - 2390480940672 n^{2} - 1875770265600}{n^{3} \left(n^{34} - 681 n^{32} + 201348 n^{30} - 34091188 n^{28} + 3674787966 n^{26} - 265541411646 n^{24} + 13212831147540 n^{22} - 458682008560740 n^{20} + 11156814277906185 n^{18} - 189688724436717985 n^{16} + 2234929793350958304 n^{14} - 17964877694273373024 n^{12} + 96171169854071114752 n^{10} - 331100792818084806912 n^{8} + 698246093019750395904 n^{6} - 842376010740646477824 n^{4} + 527127365121343488000 n^{2} - 132158898894274560000\right)}\] \[\operatorname{Wg}([6, 4, 1, 1, 1]) = \frac{210 n^{16} - 31338 n^{14} - 2714286 n^{12} + 637781010 n^{10} - 32959876428 n^{8} + 623827971264 n^{6} - 4300991551296 n^{4} + 8883663704064 n^{2} - 3119258419200}{n^{3} \left(n^{34} - 681 n^{32} + 201348 n^{30} - 34091188 n^{28} + 3674787966 n^{26} - 265541411646 n^{24} + 13212831147540 n^{22} - 458682008560740 n^{20} + 11156814277906185 n^{18} - 189688724436717985 n^{16} + 2234929793350958304 n^{14} - 17964877694273373024 n^{12} + 96171169854071114752 n^{10} - 331100792818084806912 n^{8} + 698246093019750395904 n^{6} - 842376010740646477824 n^{4} + 527127365121343488000 n^{2} - 132158898894274560000\right)}\] \[\operatorname{Wg}([5, 5, 1, 1, 1]) = \frac{196 n^{16} - 24108 n^{14} - 4197340 n^{12} + 790926836 n^{10} - 41240221848 n^{8} + 842283613192 n^{6} - 6535586661408 n^{4} + 14100956513280 n^{2} - 4257366220800}{n^{3} \left(n^{34} - 681 n^{32} + 201348 n^{30} - 34091188 n^{28} + 3674787966 n^{26} - 265541411646 n^{24} + 13212831147540 n^{22} - 458682008560740 n^{20} + 11156814277906185 n^{18} - 189688724436717985 n^{16} + 2234929793350958304 n^{14} - 17964877694273373024 n^{12} + 96171169854071114752 n^{10} - 331100792818084806912 n^{8} + 698246093019750395904 n^{6} - 842376010740646477824 n^{4} + 527127365121343488000 n^{2} - 132158898894274560000\right)}\] \[\operatorname{Wg}([10, 1, 1, 1]) = \frac{- 4862 n^{8} + 1280474 n^{6} - 103734748 n^{4} + 2589080416 n^{2} - 4660518720}{n^{2} \left(n^{28} - 655 n^{26} + 184149 n^{24} - 29192475 n^{22} + 2884568115 n^{20} - 185582594925 n^{18} + 7895987951655 n^{16} - 221607485466825 n^{14} + 4033873798269840 n^{12} - 46219318372770400 n^{10} + 319591365844102144 n^{8} - 1263559550377662720 n^{6} + 2652098870919684096 n^{4} - 2583501478797312000 n^{2} + 917770131210240000\right)}\] \[\operatorname{Wg}([3, 2, 2, 2, 2, 1, 1]) = \frac{2 n^{14} - 500 n^{12} + 52074 n^{10} - 2399312 n^{8} + 54375224 n^{6} - 646217568 n^{4} - 6231790080 n^{2} + 59918745600}{n^{3} \left(n^{30} - 559 n^{28} + 133029 n^{26} - 17794011 n^{24} + 1487822115 n^{22} - 81874038285 n^{20} + 3044172000855 n^{18} - 77386265823945 n^{16} + 1347345035281440 n^{14} - 15948891967684960 n^{12} + 126136224024338944 n^{10} - 646442435214141696 n^{8} + 2042709651000815616 n^{6} - 3670680735074156544 n^{4} + 3255175569604608000 n^{2} - 1092222304911360000\right)}\] \[\operatorname{Wg}([5, 2, 2, 2, 1, 1]) = \frac{- 14 n^{14} + 2612 n^{12} - 224502 n^{10} + 8249096 n^{8} - 132682424 n^{6} + 3507163392 n^{4} - 40950956160 n^{2} + 71817062400}{n^{2} \left(n^{32} - 560 n^{30} + 133588 n^{28} - 17927040 n^{26} + 1505616126 n^{24} - 83361860400 n^{22} + 3126046039140 n^{20} - 80430437824800 n^{18} + 1424731301105385 n^{16} - 17296237002966400 n^{14} + 142085115992023904 n^{12} - 772578659238480640 n^{10} + 2689152086214957312 n^{8} - 5713390386074972160 n^{6} + 6925856304678764544 n^{4} - 4347397874515968000 n^{2} + 1092222304911360000\right)}\] \[\operatorname{Wg}([4, 3, 2, 2, 1, 1]) = \frac{- 10 n^{10} + 1526 n^{8} - 137660 n^{6} + 4404464 n^{4} + 32639360 n^{2} - 68413440}{n^{2} \left(n^{28} - 550 n^{26} + 128079 n^{24} - 16641300 n^{22} + 1338050415 n^{20} - 69831584550 n^{18} + 2415687739905 n^{16} - 55645076164800 n^{14} + 846539349798240 n^{12} - 8330037819500800 n^{10} + 51165883648831744 n^{8} - 185949482374656000 n^{6} + 369164309628911616 n^{4} - 348201948413952000 n^{2} + 121358033879040000\right)}\] \[\operatorname{Wg}([7, 2, 2, 1, 1]) = \frac{132 n^{12} - 16874 n^{10} + 1029732 n^{8} - 19938666 n^{6} - 595135684 n^{4} + 2178799920 n^{2} + 718502400}{n^{3} \left(n^{30} - 544 n^{28} + 124884 n^{26} - 15928896 n^{24} + 1250753790 n^{22} - 63349799760 n^{20} + 2112449242980 n^{18} - 46631249937120 n^{16} + 678631302111465 n^{14} - 6438136169182960 n^{12} + 39074937285096544 n^{10} - 147379662676935936 n^{8} + 331077483383982336 n^{6} - 416150651931254784 n^{4} + 267445873778688000 n^{2} - 68263894056960000\right)}\] \[\operatorname{Wg}([3, 3, 3, 2, 1, 1]) = \frac{- 8 n^{10} + 1120 n^{8} - 121172 n^{6} + 2741724 n^{4} + 189715104 n^{2} - 1912921920}{n^{2} \left(n^{28} - 543 n^{26} + 124341 n^{24} - 15804555 n^{22} + 1234949235 n^{20} - 62114850525 n^{18} + 2050334392455 n^{16} - 44580915544665 n^{14} + 634050386566800 n^{12} - 5804085782616160 n^{10} + 33270851502480384 n^{8} - 114108811174455552 n^{6} + 216968672209526784 n^{4} - 199181979721728000 n^{2} + 68263894056960000\right)}\] \[\operatorname{Wg}([6, 3, 2, 1, 1]) = \frac{84 n^{10} - 5484 n^{8} + 365388 n^{6} - 17432196 n^{4} - 388178352 n^{2} + 3113510400}{n^{3} \left(n^{28} - 543 n^{26} + 124341 n^{24} - 15804555 n^{22} + 1234949235 n^{20} - 62114850525 n^{18} + 2050334392455 n^{16} - 44580915544665 n^{14} + 634050386566800 n^{12} - 5804085782616160 n^{10} + 33270851502480384 n^{8} - 114108811174455552 n^{6} + 216968672209526784 n^{4} - 199181979721728000 n^{2} + 68263894056960000\right)}\] \[\operatorname{Wg}([5, 4, 2, 1, 1]) = \frac{70 n^{14} - 2832 n^{12} + 125870 n^{10} - 22563076 n^{8} + 636438240 n^{6} - 9441152192 n^{4} + 45165957120 n^{2} - 2090188800}{n^{3} \left(n^{32} - 560 n^{30} + 133588 n^{28} - 17927040 n^{26} + 1505616126 n^{24} - 83361860400 n^{22} + 3126046039140 n^{20} - 80430437824800 n^{18} + 1424731301105385 n^{16} - 17296237002966400 n^{14} + 142085115992023904 n^{12} - 772578659238480640 n^{10} + 2689152086214957312 n^{8} - 5713390386074972160 n^{6} + 6925856304678764544 n^{4} - 4347397874515968000 n^{2} + 1092222304911360000\right)}\] \[\operatorname{Wg}([9, 2, 1, 1]) = \frac{- 1430 n^{6} + 138554 n^{4} - 6297876 n^{2} + 208662480}{n^{2} \left(n^{26} - 539 n^{24} + 122185 n^{22} - 15315815 n^{20} + 1173685975 n^{18} - 57420106625 n^{16} + 1820653965955 n^{14} - 37298299680845 n^{12} + 484857187843420 n^{10} - 3864657031242480 n^{8} + 17812223377510464 n^{6} - 42859917664413696 n^{4} + 45529001551872000 n^{2} - 17065973514240000\right)}\] \[\operatorname{Wg}([5, 3, 3, 1, 1]) = \frac{56 n^{14} - 2604 n^{12} + 732648 n^{10} - 83476652 n^{8} + 2215793496 n^{6} - 16657923744 n^{4} + 26957145600 n^{2} - 46680883200}{n^{3} \left(n^{32} - 560 n^{30} + 133588 n^{28} - 17927040 n^{26} + 1505616126 n^{24} - 83361860400 n^{22} + 3126046039140 n^{20} - 80430437824800 n^{18} + 1424731301105385 n^{16} - 17296237002966400 n^{14} + 142085115992023904 n^{12} - 772578659238480640 n^{10} + 2689152086214957312 n^{8} - 5713390386074972160 n^{6} + 6925856304678764544 n^{4} - 4347397874515968000 n^{2} + 1092222304911360000\right)}\] \[\operatorname{Wg}([4, 4, 3, 1, 1]) = \frac{50 n^{12} - 1460 n^{10} + 795394 n^{8} - 103845856 n^{6} + 3257598816 n^{4} - 30559348224 n^{2} + 59918745600}{n^{3} \left(n^{30} - 559 n^{28} + 133029 n^{26} - 17794011 n^{24} + 1487822115 n^{22} - 81874038285 n^{20} + 3044172000855 n^{18} - 77386265823945 n^{16} + 1347345035281440 n^{14} - 15948891967684960 n^{12} + 126136224024338944 n^{10} - 646442435214141696 n^{8} + 2042709651000815616 n^{6} - 3670680735074156544 n^{4} + 3255175569604608000 n^{2} - 1092222304911360000\right)}\] \[\operatorname{Wg}([8, 3, 1, 1]) = \frac{- 858 n^{8} + 7202 n^{6} + 3033368 n^{4} + 64583168 n^{2} - 2890168320}{n^{2} \left(n^{28} - 550 n^{26} + 128079 n^{24} - 16641300 n^{22} + 1338050415 n^{20} - 69831584550 n^{18} + 2415687739905 n^{16} - 55645076164800 n^{14} + 846539349798240 n^{12} - 8330037819500800 n^{10} + 51165883648831744 n^{8} - 185949482374656000 n^{6} + 369164309628911616 n^{4} - 348201948413952000 n^{2} + 121358033879040000\right)}\] \[\operatorname{Wg}([7, 4, 1, 1]) = \frac{- 660 n^{10} - 61494 n^{8} + 9727536 n^{6} - 178607406 n^{4} + 119408904 n^{2} + 2332774080}{n^{2} \left(n^{30} - 544 n^{28} + 124884 n^{26} - 15928896 n^{24} + 1250753790 n^{22} - 63349799760 n^{20} + 2112449242980 n^{18} - 46631249937120 n^{16} + 678631302111465 n^{14} - 6438136169182960 n^{12} + 39074937285096544 n^{10} - 147379662676935936 n^{8} + 331077483383982336 n^{6} - 416150651931254784 n^{4} + 267445873778688000 n^{2} - 68263894056960000\right)}\] \[\operatorname{Wg}([6, 5, 1, 1]) = \frac{- 588 n^{12} - 78624 n^{10} + 14611716 n^{8} - 579915672 n^{6} + 9593281152 n^{4} - 56987570304 n^{2} + 82208286720}{n^{2} \left(n^{32} - 560 n^{30} + 133588 n^{28} - 17927040 n^{26} + 1505616126 n^{24} - 83361860400 n^{22} + 3126046039140 n^{20} - 80430437824800 n^{18} + 1424731301105385 n^{16} - 17296237002966400 n^{14} + 142085115992023904 n^{12} - 772578659238480640 n^{10} + 2689152086214957312 n^{8} - 5713390386074972160 n^{6} + 6925856304678764544 n^{4} - 4347397874515968000 n^{2} + 1092222304911360000\right)}\] \[\operatorname{Wg}([11, 1, 1]) = \frac{16796 n^{2} - 1125332}{n \left(n^{24} - 530 n^{22} + 117415 n^{20} - 14259080 n^{18} + 1045354255 n^{16} - 48011918330 n^{14} + 1388546700985 n^{12} - 24801379371980 n^{10} + 261644773495600 n^{8} - 1509854069782080 n^{6} + 4223536749471744 n^{4} - 4848086919168000 n^{2} + 1896219279360000\right)}\] \[\operatorname{Wg}([2, 2, 2, 2, 2, 2, 1]) = \frac{n^{18} - 381 n^{16} + 59589 n^{14} - 4663979 n^{12} + 196118814 n^{10} - 4264059204 n^{8} + 46933559656 n^{6} - 3823605920736 n^{4} + 40980009162240 n^{2} + 24448241664000}{n^{3} \left(n^{34} - 681 n^{32} + 201348 n^{30} - 34091188 n^{28} + 3674787966 n^{26} - 265541411646 n^{24} + 13212831147540 n^{22} - 458682008560740 n^{20} + 11156814277906185 n^{18} - 189688724436717985 n^{16} + 2234929793350958304 n^{14} - 17964877694273373024 n^{12} + 96171169854071114752 n^{10} - 331100792818084806912 n^{8} + 698246093019750395904 n^{6} - 842376010740646477824 n^{4} + 527127365121343488000 n^{2} - 132158898894274560000\right)}\] \[\operatorname{Wg}([4, 2, 2, 2, 2, 1]) = \frac{- 5 n^{16} + 1519 n^{14} - 201971 n^{12} + 12988649 n^{10} - 423960748 n^{8} + 7970445020 n^{6} + 300168277104 n^{4} - 3419349314688 n^{2} - 998211962880}{n^{2} \left(n^{34} - 681 n^{32} + 201348 n^{30} - 34091188 n^{28} + 3674787966 n^{26} - 265541411646 n^{24} + 13212831147540 n^{22} - 458682008560740 n^{20} + 11156814277906185 n^{18} - 189688724436717985 n^{16} + 2234929793350958304 n^{14} - 17964877694273373024 n^{12} + 96171169854071114752 n^{10} - 331100792818084806912 n^{8} + 698246093019750395904 n^{6} - 842376010740646477824 n^{4} + 527127365121343488000 n^{2} - 132158898894274560000\right)}\] \[\operatorname{Wg}([3, 3, 2, 2, 2, 1]) = \frac{- 4 n^{16} + 1184 n^{14} - 160480 n^{12} + 10223800 n^{10} - 310139708 n^{8} + 7451192008 n^{6} + 284290173312 n^{4} - 7565988408192 n^{2} + 17549131438080}{n^{2} \left(n^{34} - 681 n^{32} + 201348 n^{30} - 34091188 n^{28} + 3674787966 n^{26} - 265541411646 n^{24} + 13212831147540 n^{22} - 458682008560740 n^{20} + 11156814277906185 n^{18} - 189688724436717985 n^{16} + 2234929793350958304 n^{14} - 17964877694273373024 n^{12} + 96171169854071114752 n^{10} - 331100792818084806912 n^{8} + 698246093019750395904 n^{6} - 842376010740646477824 n^{4} + 527127365121343488000 n^{2} - 132158898894274560000\right)}\] \[\operatorname{Wg}([6, 2, 2, 2, 1]) = \frac{42 n^{16} - 10128 n^{14} + 1112712 n^{12} - 57824124 n^{10} + 1312333950 n^{8} - 66613142868 n^{6} + 697648040496 n^{4} - 2539674881280 n^{2} - 4257366220800}{n^{3} \left(n^{34} - 681 n^{32} + 201348 n^{30} - 34091188 n^{28} + 3674787966 n^{26} - 265541411646 n^{24} + 13212831147540 n^{22} - 458682008560740 n^{20} + 11156814277906185 n^{18} - 189688724436717985 n^{16} + 2234929793350958304 n^{14} - 17964877694273373024 n^{12} + 96171169854071114752 n^{10} - 331100792818084806912 n^{8} + 698246093019750395904 n^{6} - 842376010740646477824 n^{4} + 527127365121343488000 n^{2} - 132158898894274560000\right)}\] \[\operatorname{Wg}([5, 3, 2, 2, 1]) = \frac{28 n^{14} - 5585 n^{12} + 624204 n^{10} - 34996165 n^{8} + 473926358 n^{6} - 44302789800 n^{4} + 769388146560 n^{2} + 442597478400}{n^{3} \left(n^{32} - 680 n^{30} + 200668 n^{28} - 33890520 n^{26} + 3640897446 n^{24} - 261900514200 n^{22} + 12950930633340 n^{20} - 445731077927400 n^{18} + 10711083199978785 n^{16} - 178977641236739200 n^{14} + 2055952152114219104 n^{12} - 15908925542159153920 n^{10} + 80262244311911960832 n^{8} - 250838548506172846080 n^{6} + 447407544513577549824 n^{4} - 394968466227068928000 n^{2} + 132158898894274560000\right)}\] \[\operatorname{Wg}([4, 4, 2, 2, 1]) = \frac{25 n^{16} - 4565 n^{14} + 512225 n^{12} - 31029335 n^{10} + 332380610 n^{8} - 24050900720 n^{6} + 187513836640 n^{4} + 68071979520 n^{2} + 3877996953600}{n^{3} \left(n^{34} - 681 n^{32} + 201348 n^{30} - 34091188 n^{28} + 3674787966 n^{26} - 265541411646 n^{24} + 13212831147540 n^{22} - 458682008560740 n^{20} + 11156814277906185 n^{18} - 189688724436717985 n^{16} + 2234929793350958304 n^{14} - 17964877694273373024 n^{12} + 96171169854071114752 n^{10} - 331100792818084806912 n^{8} + 698246093019750395904 n^{6} - 842376010740646477824 n^{4} + 527127365121343488000 n^{2} - 132158898894274560000\right)}\] \[\operatorname{Wg}([8, 2, 2, 1]) = \frac{- 429 n^{12} + 84656 n^{10} - 7693257 n^{8} + 335830638 n^{6} + 1887861976 n^{4} - 105849030144 n^{2} + 1071008040960}{n^{2} \left(n^{32} - 680 n^{30} + 200668 n^{28} - 33890520 n^{26} + 3640897446 n^{24} - 261900514200 n^{22} + 12950930633340 n^{20} - 445731077927400 n^{18} + 10711083199978785 n^{16} - 178977641236739200 n^{14} + 2055952152114219104 n^{12} - 15908925542159153920 n^{10} + 80262244311911960832 n^{8} - 250838548506172846080 n^{6} + 447407544513577549824 n^{4} - 394968466227068928000 n^{2} + 132158898894274560000\right)}\] \[\operatorname{Wg}([4, 3, 3, 2, 1]) = \frac{20 n^{14} - 1656 n^{12} + 363408 n^{10} + 2503240 n^{8} - 257771076 n^{6} - 2363691312 n^{4} + 38345730048 n^{2} - 56483868672}{n^{3} \left(n^{32} - 581 n^{30} + 143248 n^{28} - 19766388 n^{26} + 1698149166 n^{24} - 95726495046 n^{22} + 3640181642940 n^{20} - 94663844266740 n^{18} + 1690429851232185 n^{16} - 20645739313499485 n^{14} + 170355862001009804 n^{12} - 929291494172392624 n^{10} + 3242020436831852352 n^{8} - 6898749134899571712 n^{6} + 8371179529793224704 n^{4} - 5258057761324007424 n^{2} + 1321588988942745600\right)}\] \[\operatorname{Wg}([7, 3, 2, 1]) = \frac{- 264 n^{10} + 2750 n^{8} - 1627164 n^{6} - 53208738 n^{4} + 2393041288 n^{2} - 7527391872}{n^{2} \left(n^{30} - 572 n^{28} + 138100 n^{26} - 18523488 n^{24} + 1531437774 n^{22} - 81943555080 n^{20} + 2902689647220 n^{18} - 68539637441760 n^{16} + 1073573114256345 n^{14} - 10983581285192380 n^{12} + 71503630434278384 n^{10} - 285758820263887168 n^{8} + 670191054456867840 n^{6} - 867029644787761152 n^{4} + 567912726703374336 n^{2} - 146843220993638400\right)}\] \[\operatorname{Wg}([6, 4, 2, 1]) = \frac{- 210 n^{10} - 13368 n^{8} - 815340 n^{6} - 35416584 n^{4} - 51433650 n^{2} + 1471461552}{n^{2} \left(n^{30} - 565 n^{28} + 134208 n^{26} - 17619060 n^{24} + 1416244206 n^{22} - 73066587750 n^{20} + 2471116238940 n^{18} - 55125984443700 n^{16} + 808414100132985 n^{14} - 7711113711371725 n^{12} + 46978042619062204 n^{10} - 177642812267397360 n^{8} + 399735440553494592 n^{6} - 502982086043658240 n^{4} + 323466153094692864 n^{2} - 82599311808921600\right)}\] \[\operatorname{Wg}([5, 5, 2, 1]) = \frac{- 196 n^{12} - 14364 n^{10} - 250068 n^{8} - 14735252 n^{6} - 1128598296 n^{4} + 37978821216 n^{2} - 78348695040}{n^{2} \left(n^{32} - 581 n^{30} + 143248 n^{28} - 19766388 n^{26} + 1698149166 n^{24} - 95726495046 n^{22} + 3640181642940 n^{20} - 94663844266740 n^{18} + 1690429851232185 n^{16} - 20645739313499485 n^{14} + 170355862001009804 n^{12} - 929291494172392624 n^{10} + 3242020436831852352 n^{8} - 6898749134899571712 n^{6} + 8371179529793224704 n^{4} - 5258057761324007424 n^{2} + 1321588988942745600\right)}\] \[\operatorname{Wg}([10, 2, 1]) = \frac{4862 n^{4} - 196690 n^{2} + 22150388}{n \left(n^{26} - 555 n^{24} + 128649 n^{22} - 16327575 n^{20} + 1251810615 n^{18} - 60401533425 n^{16} + 1855834609155 n^{14} - 36024024551325 n^{12} + 431471343137340 n^{10} - 3072184059036400 n^{8} + 12372959940462144 n^{6} - 26263556331448320 n^{4} + 25743237774852096 n^{2} - 9177701312102400\right)}\] \[\operatorname{Wg}([3, 3, 3, 3, 1]) = \frac{16 n^{16} - 2896 n^{14} + 480432 n^{12} - 17236432 n^{10} - 3266822912 n^{8} + 149323318752 n^{6} - 741453227136 n^{4} - 1765106394624 n^{2} - 22298482483200}{n^{3} \left(n^{34} - 681 n^{32} + 201348 n^{30} - 34091188 n^{28} + 3674787966 n^{26} - 265541411646 n^{24} + 13212831147540 n^{22} - 458682008560740 n^{20} + 11156814277906185 n^{18} - 189688724436717985 n^{16} + 2234929793350958304 n^{14} - 17964877694273373024 n^{12} + 96171169854071114752 n^{10} - 331100792818084806912 n^{8} + 698246093019750395904 n^{6} - 842376010740646477824 n^{4} + 527127365121343488000 n^{2} - 132158898894274560000\right)}\] \[\operatorname{Wg}([6, 3, 3, 1]) = \frac{- 168 n^{14} + 11280 n^{12} - 2773536 n^{10} + 470744880 n^{8} - 12756202104 n^{6} - 56313160320 n^{4} + 1479703598208 n^{2} + 2698731509760}{n^{2} \left(n^{34} - 681 n^{32} + 201348 n^{30} - 34091188 n^{28} + 3674787966 n^{26} - 265541411646 n^{24} + 13212831147540 n^{22} - 458682008560740 n^{20} + 11156814277906185 n^{18} - 189688724436717985 n^{16} + 2234929793350958304 n^{14} - 17964877694273373024 n^{12} + 96171169854071114752 n^{10} - 331100792818084806912 n^{8} + 698246093019750395904 n^{6} - 842376010740646477824 n^{4} + 527127365121343488000 n^{2} - 132158898894274560000\right)}\] \[\operatorname{Wg}([5, 4, 3, 1]) = \frac{- 140 n^{12} + 3997 n^{10} - 2924250 n^{8} + 651867461 n^{6} - 29768172700 n^{4} + 467766271392 n^{2} - 1937023925760}{n^{2} \left(n^{32} - 680 n^{30} + 200668 n^{28} - 33890520 n^{26} + 3640897446 n^{24} - 261900514200 n^{22} + 12950930633340 n^{20} - 445731077927400 n^{18} + 10711083199978785 n^{16} - 178977641236739200 n^{14} + 2055952152114219104 n^{12} - 15908925542159153920 n^{10} + 80262244311911960832 n^{8} - 250838548506172846080 n^{6} + 447407544513577549824 n^{4} - 394968466227068928000 n^{2} + 132158898894274560000\right)}\] \[\operatorname{Wg}([9, 3, 1]) = \frac{2860 n^{10} - 98384 n^{8} - 10986404 n^{6} - 1378507416 n^{4} + 53133166944 n^{2} - 85621536000}{n^{3} \left(n^{30} - 664 n^{28} + 190044 n^{26} - 30849816 n^{24} + 3147300390 n^{22} - 211543707960 n^{20} + 9566231305980 n^{18} - 292671377031720 n^{16} + 6028341167471265 n^{14} - 82524182557198960 n^{12} + 735565231199035744 n^{10} - 4139881842974582016 n^{8} + 14024134824318648576 n^{6} - 26452391317074468864 n^{4} + 24169283440386048000 n^{2} - 8259931180892160000\right)}\] \[\operatorname{Wg}([4, 4, 4, 1]) = \frac{- 125 n^{14} + 2175 n^{12} - 3733975 n^{10} + 849305525 n^{8} - 44465885040 n^{6} + 803216500240 n^{4} - 1702323039360 n^{2} - 11386774333440}{n^{2} \left(n^{34} - 681 n^{32} + 201348 n^{30} - 34091188 n^{28} + 3674787966 n^{26} - 265541411646 n^{24} + 13212831147540 n^{22} - 458682008560740 n^{20} + 11156814277906185 n^{18} - 189688724436717985 n^{16} + 2234929793350958304 n^{14} - 17964877694273373024 n^{12} + 96171169854071114752 n^{10} - 331100792818084806912 n^{8} + 698246093019750395904 n^{6} - 842376010740646477824 n^{4} + 527127365121343488000 n^{2} - 132158898894274560000\right)}\] \[\operatorname{Wg}([8, 4, 1]) = \frac{2145 n^{12} + 154154 n^{10} - 54566655 n^{8} + 1726668372 n^{6} + 5261644960 n^{4} - 792465163776 n^{2} + 4383822643200}{n^{3} \left(n^{32} - 680 n^{30} + 200668 n^{28} - 33890520 n^{26} + 3640897446 n^{24} - 261900514200 n^{22} + 12950930633340 n^{20} - 445731077927400 n^{18} + 10711083199978785 n^{16} - 178977641236739200 n^{14} + 2055952152114219104 n^{12} - 15908925542159153920 n^{10} + 80262244311911960832 n^{8} - 250838548506172846080 n^{6} + 447407544513577549824 n^{4} - 394968466227068928000 n^{2} + 132158898894274560000\right)}\] \[\operatorname{Wg}([7, 5, 1]) = \frac{1848 n^{12} + 297990 n^{10} - 81505116 n^{8} + 4154287830 n^{6} - 99837477432 n^{4} + 1021754321280 n^{2} - 1180259942400}{n^{3} \left(n^{32} - 680 n^{30} + 200668 n^{28} - 33890520 n^{26} + 3640897446 n^{24} - 261900514200 n^{22} + 12950930633340 n^{20} - 445731077927400 n^{18} + 10711083199978785 n^{16} - 178977641236739200 n^{14} + 2055952152114219104 n^{12} - 15908925542159153920 n^{10} + 80262244311911960832 n^{8} - 250838548506172846080 n^{6} + 447407544513577549824 n^{4} - 394968466227068928000 n^{2} + 132158898894274560000\right)}\] \[\operatorname{Wg}([6, 6, 1]) = \frac{1764 n^{12} + 341712 n^{10} - 90525708 n^{8} + 5084578296 n^{6} - 149010001056 n^{4} + 2204161569792 n^{2} - 9147014553600}{n^{3} \left(n^{32} - 680 n^{30} + 200668 n^{28} - 33890520 n^{26} + 3640897446 n^{24} - 261900514200 n^{22} + 12950930633340 n^{20} - 445731077927400 n^{18} + 10711083199978785 n^{16} - 178977641236739200 n^{14} + 2055952152114219104 n^{12} - 15908925542159153920 n^{10} + 80262244311911960832 n^{8} - 250838548506172846080 n^{6} + 447407544513577549824 n^{4} - 394968466227068928000 n^{2} + 132158898894274560000\right)}\] \[\operatorname{Wg}([12, 1]) = \frac{- 58786 n^{2} + 5969040}{n^{2} \left(n^{24} - 650 n^{22} + 180895 n^{20} - 28285400 n^{18} + 2742417535 n^{16} - 171757365650 n^{14} + 7026231453265 n^{12} - 185789298737900 n^{10} + 3076822378767280 n^{8} - 30092049283982400 n^{6} + 156823829909121024 n^{4} - 359072203696128000 n^{2} + 229442532802560000\right)}\] \[\operatorname{Wg}([3, 2, 2, 2, 2, 2]) = \frac{- 2 n^{16} + 622 n^{14} - 86918 n^{12} + 5334818 n^{10} - 228742048 n^{8} - 827540392 n^{6} - 368177074752 n^{4} + 5869598919552 n^{2} - 46598708090880}{n^{2} \left(n^{34} - 681 n^{32} + 201348 n^{30} - 34091188 n^{28} + 3674787966 n^{26} - 265541411646 n^{24} + 13212831147540 n^{22} - 458682008560740 n^{20} + 11156814277906185 n^{18} - 189688724436717985 n^{16} + 2234929793350958304 n^{14} - 17964877694273373024 n^{12} + 96171169854071114752 n^{10} - 331100792818084806912 n^{8} + 698246093019750395904 n^{6} - 842376010740646477824 n^{4} + 527127365121343488000 n^{2} - 132158898894274560000\right)}\] \[\operatorname{Wg}([5, 2, 2, 2, 2]) = \frac{14 n^{16} - 3226 n^{14} + 399314 n^{12} - 16349558 n^{10} + 935565880 n^{8} + 27430995544 n^{6} + 177761292192 n^{4} - 3536131023360 n^{2} - 4889648332800}{n^{3} \left(n^{34} - 681 n^{32} + 201348 n^{30} - 34091188 n^{28} + 3674787966 n^{26} - 265541411646 n^{24} + 13212831147540 n^{22} - 458682008560740 n^{20} + 11156814277906185 n^{18} - 189688724436717985 n^{16} + 2234929793350958304 n^{14} - 17964877694273373024 n^{12} + 96171169854071114752 n^{10} - 331100792818084806912 n^{8} + 698246093019750395904 n^{6} - 842376010740646477824 n^{4} + 527127365121343488000 n^{2} - 132158898894274560000\right)}\] \[\operatorname{Wg}([4, 3, 2, 2, 2]) = \frac{10 n^{16} - 2090 n^{14} + 285010 n^{12} - 9450190 n^{10} + 698894300 n^{8} + 25837241600 n^{6} - 893110950720 n^{4} + 8158904340480 n^{2} + 927347097600}{n^{3} \left(n^{34} - 681 n^{32} + 201348 n^{30} - 34091188 n^{28} + 3674787966 n^{26} - 265541411646 n^{24} + 13212831147540 n^{22} - 458682008560740 n^{20} + 11156814277906185 n^{18} - 189688724436717985 n^{16} + 2234929793350958304 n^{14} - 17964877694273373024 n^{12} + 96171169854071114752 n^{10} - 331100792818084806912 n^{8} + 698246093019750395904 n^{6} - 842376010740646477824 n^{4} + 527127365121343488000 n^{2} - 132158898894274560000\right)}\] \[\operatorname{Wg}([7, 2, 2, 2]) = \frac{- 132 n^{14} + 22308 n^{12} - 2537172 n^{10} + 46229964 n^{8} - 5214600600 n^{6} - 5217962112 n^{4} - 170546023296 n^{2} + 12510436055040}{n^{2} \left(n^{34} - 681 n^{32} + 201348 n^{30} - 34091188 n^{28} + 3674787966 n^{26} - 265541411646 n^{24} + 13212831147540 n^{22} - 458682008560740 n^{20} + 11156814277906185 n^{18} - 189688724436717985 n^{16} + 2234929793350958304 n^{14} - 17964877694273373024 n^{12} + 96171169854071114752 n^{10} - 331100792818084806912 n^{8} + 698246093019750395904 n^{6} - 842376010740646477824 n^{4} + 527127365121343488000 n^{2} - 132158898894274560000\right)}\] \[\operatorname{Wg}([3, 3, 3, 2, 2]) = \frac{8 n^{16} - 1640 n^{14} + 247464 n^{12} - 5912888 n^{10} + 604907888 n^{8} + 14851635456 n^{6} - 1865951948160 n^{4} + 16245457155072 n^{2} - 26724457267200}{n^{3} \left(n^{34} - 681 n^{32} + 201348 n^{30} - 34091188 n^{28} + 3674787966 n^{26} - 265541411646 n^{24} + 13212831147540 n^{22} - 458682008560740 n^{20} + 11156814277906185 n^{18} - 189688724436717985 n^{16} + 2234929793350958304 n^{14} - 17964877694273373024 n^{12} + 96171169854071114752 n^{10} - 331100792818084806912 n^{8} + 698246093019750395904 n^{6} - 842376010740646477824 n^{4} + 527127365121343488000 n^{2} - 132158898894274560000\right)}\] \[\operatorname{Wg}([6, 3, 2, 2]) = \frac{- 84 n^{14} + 9324 n^{12} - 1453452 n^{10} + 1906212 n^{8} - 4044713904 n^{6} + 118060260864 n^{4} + 269185271040 n^{2} - 4493035008000}{n^{2} \left(n^{34} - 681 n^{32} + 201348 n^{30} - 34091188 n^{28} + 3674787966 n^{26} - 265541411646 n^{24} + 13212831147540 n^{22} - 458682008560740 n^{20} + 11156814277906185 n^{18} - 189688724436717985 n^{16} + 2234929793350958304 n^{14} - 17964877694273373024 n^{12} + 96171169854071114752 n^{10} - 331100792818084806912 n^{8} + 698246093019750395904 n^{6} - 842376010740646477824 n^{4} + 527127365121343488000 n^{2} - 132158898894274560000\right)}\] \[\operatorname{Wg}([5, 4, 2, 2]) = \frac{- 70 n^{14} + 4950 n^{12} - 1063070 n^{10} - 5982110 n^{8} - 3486621540 n^{6} + 52274374160 n^{4} - 106336936320 n^{2} - 8162111232000}{n^{2} \left(n^{34} - 681 n^{32} + 201348 n^{30} - 34091188 n^{28} + 3674787966 n^{26} - 265541411646 n^{24} + 13212831147540 n^{22} - 458682008560740 n^{20} + 11156814277906185 n^{18} - 189688724436717985 n^{16} + 2234929793350958304 n^{14} - 17964877694273373024 n^{12} + 96171169854071114752 n^{10} - 331100792818084806912 n^{8} + 698246093019750395904 n^{6} - 842376010740646477824 n^{4} + 527127365121343488000 n^{2} - 132158898894274560000\right)}\] \[\operatorname{Wg}([9, 2, 2]) = \frac{1430 n^{10} - 151840 n^{8} + 17565470 n^{6} + 187877820 n^{4} + 8230837680 n^{2} + 171243072000}{n^{3} \left(n^{30} - 664 n^{28} + 190044 n^{26} - 30849816 n^{24} + 3147300390 n^{22} - 211543707960 n^{20} + 9566231305980 n^{18} - 292671377031720 n^{16} + 6028341167471265 n^{14} - 82524182557198960 n^{12} + 735565231199035744 n^{10} - 4139881842974582016 n^{8} + 14024134824318648576 n^{6} - 26452391317074468864 n^{4} + 24169283440386048000 n^{2} - 8259931180892160000\right)}\] \[\operatorname{Wg}([5, 3, 3, 2]) = \frac{- 56 n^{14} + 4388 n^{12} - 1453500 n^{10} + 983564 n^{8} - 1371434012 n^{6} + 147252509088 n^{4} - 682147991232 n^{2} + 4646101109760}{n^{2} \left(n^{34} - 681 n^{32} + 201348 n^{30} - 34091188 n^{28} + 3674787966 n^{26} - 265541411646 n^{24} + 13212831147540 n^{22} - 458682008560740 n^{20} + 11156814277906185 n^{18} - 189688724436717985 n^{16} + 2234929793350958304 n^{14} - 17964877694273373024 n^{12} + 96171169854071114752 n^{10} - 331100792818084806912 n^{8} + 698246093019750395904 n^{6} - 842376010740646477824 n^{4} + 527127365121343488000 n^{2} - 132158898894274560000\right)}\] \[\operatorname{Wg}([4, 4, 3, 2]) = \frac{- 50 n^{14} + 3150 n^{12} - 1463950 n^{10} + 6310490 n^{8} - 93326280 n^{6} + 55023426400 n^{4} - 2199423592320 n^{2} + 10364156098560}{n^{2} \left(n^{34} - 681 n^{32} + 201348 n^{30} - 34091188 n^{28} + 3674787966 n^{26} - 265541411646 n^{24} + 13212831147540 n^{22} - 458682008560740 n^{20} + 11156814277906185 n^{18} - 189688724436717985 n^{16} + 2234929793350958304 n^{14} - 17964877694273373024 n^{12} + 96171169854071114752 n^{10} - 331100792818084806912 n^{8} + 698246093019750395904 n^{6} - 842376010740646477824 n^{4} + 527127365121343488000 n^{2} - 132158898894274560000\right)}\] \[\operatorname{Wg}([8, 3, 2]) = \frac{858 n^{12} - 22932 n^{10} + 8386794 n^{8} + 349303344 n^{6} - 27397405152 n^{4} + 385760613888 n^{2} - 4383822643200}{n^{3} \left(n^{32} - 680 n^{30} + 200668 n^{28} - 33890520 n^{26} + 3640897446 n^{24} - 261900514200 n^{22} + 12950930633340 n^{20} - 445731077927400 n^{18} + 10711083199978785 n^{16} - 178977641236739200 n^{14} + 2055952152114219104 n^{12} - 15908925542159153920 n^{10} + 80262244311911960832 n^{8} - 250838548506172846080 n^{6} + 447407544513577549824 n^{4} - 394968466227068928000 n^{2} + 132158898894274560000\right)}\] \[\operatorname{Wg}([7, 4, 2]) = \frac{660 n^{14} + 43300 n^{12} + 1565660 n^{10} + 469182540 n^{8} - 19279726240 n^{6} + 345057914560 n^{4} + 706478469120 n^{2} - 5142561177600}{n^{3} \left(n^{34} - 681 n^{32} + 201348 n^{30} - 34091188 n^{28} + 3674787966 n^{26} - 265541411646 n^{24} + 13212831147540 n^{22} - 458682008560740 n^{20} + 11156814277906185 n^{18} - 189688724436717985 n^{16} + 2234929793350958304 n^{14} - 17964877694273373024 n^{12} + 96171169854071114752 n^{10} - 331100792818084806912 n^{8} + 698246093019750395904 n^{6} - 842376010740646477824 n^{4} + 527127365121343488000 n^{2} - 132158898894274560000\right)}\] \[\operatorname{Wg}([6, 5, 2]) = \frac{588 n^{12} + 80640 n^{10} - 528696 n^{8} + 516299280 n^{6} + 4075351308 n^{4} - 402402031920 n^{2} + 123821913600}{n^{3} \left(n^{32} - 665 n^{30} + 190708 n^{28} - 31039860 n^{26} + 3178150206 n^{24} - 214691008350 n^{22} + 9777775013940 n^{20} - 302237608337700 n^{18} + 6321012544502985 n^{16} - 88552523724670225 n^{14} + 818089413756234704 n^{12} - 4875447074173617760 n^{10} + 18164016667293230592 n^{8} - 40476526141393117440 n^{6} + 50621674757460516864 n^{4} - 32429214621278208000 n^{2} + 8259931180892160000\right)}\] \[\operatorname{Wg}([11, 2]) = \frac{- 16796 n^{4} + 869516 n^{2} - 133877040}{n^{2} \left(n^{26} - 651 n^{24} + 181545 n^{22} - 28466295 n^{20} + 2770702935 n^{18} - 174499783185 n^{16} + 7197988818915 n^{14} - 192815530191165 n^{12} + 3262611677505180 n^{10} - 33168871662749680 n^{8} + 186915879193103424 n^{6} - 515896033605249024 n^{4} + 588514736498688000 n^{2} - 229442532802560000\right)}\] \[\operatorname{Wg}([4, 3, 3, 3]) = \frac{- 40 n^{14} + 2680 n^{12} - 1403160 n^{10} - 85879640 n^{8} + 9833347040 n^{6} - 55637645760 n^{4} - 2886674826240 n^{2} - 9396934778880}{n^{2} \left(n^{34} - 681 n^{32} + 201348 n^{30} - 34091188 n^{28} + 3674787966 n^{26} - 265541411646 n^{24} + 13212831147540 n^{22} - 458682008560740 n^{20} + 11156814277906185 n^{18} - 189688724436717985 n^{16} + 2234929793350958304 n^{14} - 17964877694273373024 n^{12} + 96171169854071114752 n^{10} - 331100792818084806912 n^{8} + 698246093019750395904 n^{6} - 842376010740646477824 n^{4} + 527127365121343488000 n^{2} - 132158898894274560000\right)}\] \[\operatorname{Wg}([7, 3, 3]) = \frac{528 n^{14} + 21648 n^{12} + 14029488 n^{10} - 433845456 n^{8} - 28651180800 n^{6} + 692837025408 n^{4} - 368701065216 n^{2} + 7924602470400}{n^{3} \left(n^{34} - 681 n^{32} + 201348 n^{30} - 34091188 n^{28} + 3674787966 n^{26} - 265541411646 n^{24} + 13212831147540 n^{22} - 458682008560740 n^{20} + 11156814277906185 n^{18} - 189688724436717985 n^{16} + 2234929793350958304 n^{14} - 17964877694273373024 n^{12} + 96171169854071114752 n^{10} - 331100792818084806912 n^{8} + 698246093019750395904 n^{6} - 842376010740646477824 n^{4} + 527127365121343488000 n^{2} - 132158898894274560000\right)}\] \[\operatorname{Wg}([6, 4, 3]) = \frac{420 n^{14} + 43092 n^{12} + 16239468 n^{10} - 1180295844 n^{8} + 20569256064 n^{6} - 72350499648 n^{4} + 3108975464448 n^{2} - 7165863936000}{n^{3} \left(n^{34} - 681 n^{32} + 201348 n^{30} - 34091188 n^{28} + 3674787966 n^{26} - 265541411646 n^{24} + 13212831147540 n^{22} - 458682008560740 n^{20} + 11156814277906185 n^{18} - 189688724436717985 n^{16} + 2234929793350958304 n^{14} - 17964877694273373024 n^{12} + 96171169854071114752 n^{10} - 331100792818084806912 n^{8} + 698246093019750395904 n^{6} - 842376010740646477824 n^{4} + 527127365121343488000 n^{2} - 132158898894274560000\right)}\] \[\operatorname{Wg}([5, 5, 3]) = \frac{392 n^{14} + 49588 n^{12} + 16832676 n^{10} - 1462634516 n^{8} + 46795388612 n^{6} - 804100509072 n^{4} + 84316619520 n^{2} - 7545233203200}{n^{3} \left(n^{34} - 681 n^{32} + 201348 n^{30} - 34091188 n^{28} + 3674787966 n^{26} - 265541411646 n^{24} + 13212831147540 n^{22} - 458682008560740 n^{20} + 11156814277906185 n^{18} - 189688724436717985 n^{16} + 2234929793350958304 n^{14} - 17964877694273373024 n^{12} + 96171169854071114752 n^{10} - 331100792818084806912 n^{8} + 698246093019750395904 n^{6} - 842376010740646477824 n^{4} + 527127365121343488000 n^{2} - 132158898894274560000\right)}\] \[\operatorname{Wg}([10, 3]) = \frac{- 9724 n^{6} - 714340 n^{4} - 73238176 n^{2} + 4421757120}{n^{2} \left(n^{28} - 655 n^{26} + 184149 n^{24} - 29192475 n^{22} + 2884568115 n^{20} - 185582594925 n^{18} + 7895987951655 n^{16} - 221607485466825 n^{14} + 4033873798269840 n^{12} - 46219318372770400 n^{10} + 319591365844102144 n^{8} - 1263559550377662720 n^{6} + 2652098870919684096 n^{4} - 2583501478797312000 n^{2} + 917770131210240000\right)}\] \[\operatorname{Wg}([5, 4, 4]) = \frac{350 n^{14} + 46550 n^{12} + 21611450 n^{10} - 2162447630 n^{8} + 73658092480 n^{6} - 468033698720 n^{4} - 8076063905280 n^{2} + 16692247756800}{n^{3} \left(n^{34} - 681 n^{32} + 201348 n^{30} - 34091188 n^{28} + 3674787966 n^{26} - 265541411646 n^{24} + 13212831147540 n^{22} - 458682008560740 n^{20} + 11156814277906185 n^{18} - 189688724436717985 n^{16} + 2234929793350958304 n^{14} - 17964877694273373024 n^{12} + 96171169854071114752 n^{10} - 331100792818084806912 n^{8} + 698246093019750395904 n^{6} - 842376010740646477824 n^{4} + 527127365121343488000 n^{2} - 132158898894274560000\right)}\] \[\operatorname{Wg}([9, 4]) = \frac{- 7150 n^{8} - 1523500 n^{6} + 30616850 n^{4} + 2477403720 n^{2} - 114429775680}{n^{2} \left(n^{30} - 664 n^{28} + 190044 n^{26} - 30849816 n^{24} + 3147300390 n^{22} - 211543707960 n^{20} + 9566231305980 n^{18} - 292671377031720 n^{16} + 6028341167471265 n^{14} - 82524182557198960 n^{12} + 735565231199035744 n^{10} - 4139881842974582016 n^{8} + 14024134824318648576 n^{6} - 26452391317074468864 n^{4} + 24169283440386048000 n^{2} - 8259931180892160000\right)}\] \[\operatorname{Wg}([8, 5]) = \frac{- 6006 n^{10} - 1926540 n^{8} + 142282602 n^{6} - 4606241640 n^{4} + 45636079104 n^{2} + 812450580480}{n^{2} \left(n^{32} - 680 n^{30} + 200668 n^{28} - 33890520 n^{26} + 3640897446 n^{24} - 261900514200 n^{22} + 12950930633340 n^{20} - 445731077927400 n^{18} + 10711083199978785 n^{16} - 178977641236739200 n^{14} + 2055952152114219104 n^{12} - 15908925542159153920 n^{10} + 80262244311911960832 n^{8} - 250838548506172846080 n^{6} + 447407544513577549824 n^{4} - 394968466227068928000 n^{2} + 132158898894274560000\right)}\] \[\operatorname{Wg}([7, 6]) = \frac{- 5544 n^{10} - 2162160 n^{8} + 189421848 n^{6} - 9227877120 n^{4} + 267557786496 n^{2} - 3360611358720}{n^{2} \left(n^{32} - 680 n^{30} + 200668 n^{28} - 33890520 n^{26} + 3640897446 n^{24} - 261900514200 n^{22} + 12950930633340 n^{20} - 445731077927400 n^{18} + 10711083199978785 n^{16} - 178977641236739200 n^{14} + 2055952152114219104 n^{12} - 15908925542159153920 n^{10} + 80262244311911960832 n^{8} - 250838548506172846080 n^{6} + 447407544513577549824 n^{4} - 394968466227068928000 n^{2} + 132158898894274560000\right)}\] \[\operatorname{Wg}([13]) = \frac{208012}{n \left(n^{24} - 650 n^{22} + 180895 n^{20} - 28285400 n^{18} + 2742417535 n^{16} - 171757365650 n^{14} + 7026231453265 n^{12} - 185789298737900 n^{10} + 3076822378767280 n^{8} - 30092049283982400 n^{6} + 156823829909121024 n^{4} - 359072203696128000 n^{2} + 229442532802560000\right)}\]