Weingarten functions for p = 12
Below are the values of the Weingarten function for permutation size p = 12. The input is given as a partition of p. You can also download them as a text file or as a python pickle file.
\[\operatorname{Wg}([1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]) = \frac{n^{22} - 471 n^{20} + 91889 n^{18} - 9664659 n^{16} + 598608438 n^{14} - 22463586558 n^{12} + 508927847468 n^{10} - 6771913965708 n^{8} + 50041272365224 n^{6} - 184428527224104 n^{4} + 276420131131680 n^{2} - 89275280371200}{n^{2} \left(n^{32} - 537 n^{30} + 124020 n^{28} - 16232308 n^{26} + 1337335614 n^{24} - 72965083230 n^{22} + 2705859162420 n^{20} - 69038289172260 n^{18} + 1215300637100745 n^{16} - 14685432694210705 n^{14} + 120227485384616784 n^{12} - 652119798888556128 n^{10} + 2265918814119032320 n^{8} - 4808483584944152832 n^{6} + 5824456787792388096 n^{4} - 3654233298542592000 n^{2} + 917770131210240000\right)}\]
\[\operatorname{Wg}([2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]) = \frac{- n^{22} + 451 n^{20} - 83319 n^{18} + 8180709 n^{16} - 464432088 n^{14} + 15606424128 n^{12} - 307376461988 n^{10} + 3420847183148 n^{8} - 19982577687264 n^{6} + 53099480009664 n^{4} - 47298964055040 n^{2} + 6828646809600}{n^{3} \left(n^{32} - 537 n^{30} + 124020 n^{28} - 16232308 n^{26} + 1337335614 n^{24} - 72965083230 n^{22} + 2705859162420 n^{20} - 69038289172260 n^{18} + 1215300637100745 n^{16} - 14685432694210705 n^{14} + 120227485384616784 n^{12} - 652119798888556128 n^{10} + 2265918814119032320 n^{8} - 4808483584944152832 n^{6} + 5824456787792388096 n^{4} - 3654233298542592000 n^{2} + 917770131210240000\right)}\]
\[\operatorname{Wg}([3, 1, 1, 1, 1, 1, 1, 1, 1, 1]) = \frac{2 n^{20} - 857 n^{18} + 148395 n^{16} - 13417635 n^{14} + 685716243 n^{12} - 20155138548 n^{10} + 335106678256 n^{8} - 3005869467796 n^{6} + 13132904721444 n^{4} - 22912116707664 n^{2} + 8244663356160}{n^{2} \left(n^{32} - 537 n^{30} + 124020 n^{28} - 16232308 n^{26} + 1337335614 n^{24} - 72965083230 n^{22} + 2705859162420 n^{20} - 69038289172260 n^{18} + 1215300637100745 n^{16} - 14685432694210705 n^{14} + 120227485384616784 n^{12} - 652119798888556128 n^{10} + 2265918814119032320 n^{8} - 4808483584944152832 n^{6} + 5824456787792388096 n^{4} - 3654233298542592000 n^{2} + 917770131210240000\right)}\]
\[\operatorname{Wg}([2, 2, 1, 1, 1, 1, 1, 1, 1, 1]) = \frac{n^{20} - 425 n^{18} + 72969 n^{16} - 6545119 n^{14} + 332403478 n^{12} - 9740132944 n^{10} + 161991244548 n^{8} - 1454812629140 n^{6} + 6390734016424 n^{4} - 11596783647072 n^{2} + 7916549921280}{n^{2} \left(n^{32} - 537 n^{30} + 124020 n^{28} - 16232308 n^{26} + 1337335614 n^{24} - 72965083230 n^{22} + 2705859162420 n^{20} - 69038289172260 n^{18} + 1215300637100745 n^{16} - 14685432694210705 n^{14} + 120227485384616784 n^{12} - 652119798888556128 n^{10} + 2265918814119032320 n^{8} - 4808483584944152832 n^{6} + 5824456787792388096 n^{4} - 3654233298542592000 n^{2} + 917770131210240000\right)}\]
\[\operatorname{Wg}([4, 1, 1, 1, 1, 1, 1, 1, 1]) = \frac{- 5 n^{20} + 2027 n^{18} - 327087 n^{16} + 27016437 n^{14} - 1228634412 n^{12} + 31071805080 n^{10} - 426202766500 n^{8} + 2981361183676 n^{6} - 9254093701296 n^{4} + 9594807194880 n^{2} - 1517477068800}{n^{3} \left(n^{32} - 537 n^{30} + 124020 n^{28} - 16232308 n^{26} + 1337335614 n^{24} - 72965083230 n^{22} + 2705859162420 n^{20} - 69038289172260 n^{18} + 1215300637100745 n^{16} - 14685432694210705 n^{14} + 120227485384616784 n^{12} - 652119798888556128 n^{10} + 2265918814119032320 n^{8} - 4808483584944152832 n^{6} + 5824456787792388096 n^{4} - 3654233298542592000 n^{2} + 917770131210240000\right)}\]
\[\operatorname{Wg}([3, 2, 1, 1, 1, 1, 1, 1, 1]) = \frac{- 2 n^{18} + 785 n^{16} - 121892 n^{14} + 9627575 n^{12} - 416500220 n^{10} + 9988700690 n^{8} - 129214926936 n^{6} + 824425236000 n^{4} - 2049888384000 n^{2} + 474211584000}{n^{3} \left(n^{30} - 536 n^{28} + 123484 n^{26} - 16108824 n^{24} + 1321226790 n^{22} - 71643856440 n^{20} + 2634215305980 n^{18} - 66404073866280 n^{16} + 1148896563234465 n^{14} - 13536536130976240 n^{12} + 106690949253640544 n^{10} - 545428849634915584 n^{8} + 1720489964484116736 n^{6} - 3087993620460036096 n^{4} + 2736463167332352000 n^{2} - 917770131210240000\right)}\]
\[\operatorname{Wg}([5, 1, 1, 1, 1, 1, 1, 1]) = \frac{14 n^{18} - 5334 n^{16} + 795494 n^{14} - 59400194 n^{12} + 2372325620 n^{10} - 50750229320 n^{8} + 560648797632 n^{6} - 2925306219752 n^{4} + 5978276233440 n^{2} - 2861049945600}{n^{2} \left(n^{32} - 537 n^{30} + 124020 n^{28} - 16232308 n^{26} + 1337335614 n^{24} - 72965083230 n^{22} + 2705859162420 n^{20} - 69038289172260 n^{18} + 1215300637100745 n^{16} - 14685432694210705 n^{14} + 120227485384616784 n^{12} - 652119798888556128 n^{10} + 2265918814119032320 n^{8} - 4808483584944152832 n^{6} + 5824456787792388096 n^{4} - 3654233298542592000 n^{2} + 917770131210240000\right)}\]
\[\operatorname{Wg}([2, 2, 2, 1, 1, 1, 1, 1, 1]) = \frac{- n^{20} + 393 n^{18} - 61543 n^{16} + 4961773 n^{14} - 223008352 n^{12} + 5670692110 n^{10} - 78979950108 n^{8} + 553765828384 n^{6} - 1734776277696 n^{4} + 2697290634240 n^{2} - 1643933491200}{n^{3} \left(n^{32} - 537 n^{30} + 124020 n^{28} - 16232308 n^{26} + 1337335614 n^{24} - 72965083230 n^{22} + 2705859162420 n^{20} - 69038289172260 n^{18} + 1215300637100745 n^{16} - 14685432694210705 n^{14} + 120227485384616784 n^{12} - 652119798888556128 n^{10} + 2265918814119032320 n^{8} - 4808483584944152832 n^{6} + 5824456787792388096 n^{4} - 3654233298542592000 n^{2} + 917770131210240000\right)}\]
\[\operatorname{Wg}([4, 2, 1, 1, 1, 1, 1, 1]) = \frac{5 n^{16} - 1719 n^{14} + 222465 n^{12} - 13566099 n^{10} + 401572950 n^{8} - 5471747490 n^{6} + 31693111600 n^{4} - 72416210592 n^{2} + 86042753280}{n^{2} \left(n^{30} - 521 n^{28} + 115684 n^{26} - 14381364 n^{24} + 1107233790 n^{22} - 55249342590 n^{20} + 1821869680980 n^{18} - 39888374276580 n^{16} + 577086648675465 n^{14} - 5452046315403265 n^{12} + 32994744338164544 n^{10} - 124203889477923424 n^{8} + 278656582472257536 n^{6} - 349978265388032256 n^{4} + 224804541583872000 n^{2} - 57360633200640000\right)}\]
\[\operatorname{Wg}([3, 3, 1, 1, 1, 1, 1, 1]) = \frac{4 n^{18} - 1388 n^{16} + 183098 n^{14} - 11626838 n^{12} + 376137254 n^{10} - 6236051810 n^{8} + 52897558852 n^{6} - 211810348884 n^{4} + 350455434192 n^{2} + 116099723520}{n^{2} \left(n^{32} - 537 n^{30} + 124020 n^{28} - 16232308 n^{26} + 1337335614 n^{24} - 72965083230 n^{22} + 2705859162420 n^{20} - 69038289172260 n^{18} + 1215300637100745 n^{16} - 14685432694210705 n^{14} + 120227485384616784 n^{12} - 652119798888556128 n^{10} + 2265918814119032320 n^{8} - 4808483584944152832 n^{6} + 5824456787792388096 n^{4} - 3654233298542592000 n^{2} + 917770131210240000\right)}\]
\[\operatorname{Wg}([6, 1, 1, 1, 1, 1, 1]) = \frac{- 42 n^{18} + 14862 n^{16} - 2018802 n^{14} + 133885542 n^{12} - 4600540380 n^{10} + 81451998660 n^{8} - 706385210496 n^{6} + 2611219772736 n^{4} - 3053823482880 n^{2} + 569053900800}{n^{3} \left(n^{32} - 537 n^{30} + 124020 n^{28} - 16232308 n^{26} + 1337335614 n^{24} - 72965083230 n^{22} + 2705859162420 n^{20} - 69038289172260 n^{18} + 1215300637100745 n^{16} - 14685432694210705 n^{14} + 120227485384616784 n^{12} - 652119798888556128 n^{10} + 2265918814119032320 n^{8} - 4808483584944152832 n^{6} + 5824456787792388096 n^{4} - 3654233298542592000 n^{2} + 917770131210240000\right)}\]
\[\operatorname{Wg}([3, 2, 2, 1, 1, 1, 1, 1]) = \frac{2 n^{18} - 705 n^{16} + 97245 n^{14} - 6815495 n^{12} + 265819783 n^{10} - 5903939280 n^{8} + 70680419166 n^{6} - 389655625660 n^{4} + 653447420304 n^{2} - 127646703360}{n^{2} \left(n^{32} - 537 n^{30} + 124020 n^{28} - 16232308 n^{26} + 1337335614 n^{24} - 72965083230 n^{22} + 2705859162420 n^{20} - 69038289172260 n^{18} + 1215300637100745 n^{16} - 14685432694210705 n^{14} + 120227485384616784 n^{12} - 652119798888556128 n^{10} + 2265918814119032320 n^{8} - 4808483584944152832 n^{6} + 5824456787792388096 n^{4} - 3654233298542592000 n^{2} + 917770131210240000\right)}\]
\[\operatorname{Wg}([5, 2, 1, 1, 1, 1, 1]) = \frac{- 14 n^{18} + 4534 n^{16} - 549594 n^{14} + 31477054 n^{12} - 897183080 n^{10} + 12540356100 n^{8} - 78128289512 n^{6} + 169376974912 n^{4} - 43526592000 n^{2} + 242374809600}{n^{3} \left(n^{32} - 537 n^{30} + 124020 n^{28} - 16232308 n^{26} + 1337335614 n^{24} - 72965083230 n^{22} + 2705859162420 n^{20} - 69038289172260 n^{18} + 1215300637100745 n^{16} - 14685432694210705 n^{14} + 120227485384616784 n^{12} - 652119798888556128 n^{10} + 2265918814119032320 n^{8} - 4808483584944152832 n^{6} + 5824456787792388096 n^{4} - 3654233298542592000 n^{2} + 917770131210240000\right)}\]
\[\operatorname{Wg}([4, 3, 1, 1, 1, 1, 1]) = \frac{- 10 n^{18} + 2945 n^{16} - 302615 n^{14} + 12410285 n^{12} - 128788145 n^{10} - 3141049930 n^{8} + 70614275750 n^{6} - 405914585400 n^{4} + 666195131520 n^{2} - 126456422400}{n^{3} \left(n^{32} - 537 n^{30} + 124020 n^{28} - 16232308 n^{26} + 1337335614 n^{24} - 72965083230 n^{22} + 2705859162420 n^{20} - 69038289172260 n^{18} + 1215300637100745 n^{16} - 14685432694210705 n^{14} + 120227485384616784 n^{12} - 652119798888556128 n^{10} + 2265918814119032320 n^{8} - 4808483584944152832 n^{6} + 5824456787792388096 n^{4} - 3654233298542592000 n^{2} + 917770131210240000\right)}\]
\[\operatorname{Wg}([7, 1, 1, 1, 1, 1]) = \frac{132 n^{14} - 42405 n^{12} + 5089722 n^{10} - 287828475 n^{8} + 8058561720 n^{6} - 109656786030 n^{4} + 658712381976 n^{2} - 1298385728640}{n^{2} \left(n^{30} - 536 n^{28} + 123484 n^{26} - 16108824 n^{24} + 1321226790 n^{22} - 71643856440 n^{20} + 2634215305980 n^{18} - 66404073866280 n^{16} + 1148896563234465 n^{14} - 13536536130976240 n^{12} + 106690949253640544 n^{10} - 545428849634915584 n^{8} + 1720489964484116736 n^{6} - 3087993620460036096 n^{4} + 2736463167332352000 n^{2} - 917770131210240000\right)}\]
\[\operatorname{Wg}([2, 2, 2, 2, 1, 1, 1, 1]) = \frac{n^{18} - 355 n^{16} + 49853 n^{14} - 3573975 n^{12} + 139423510 n^{10} - 2855511290 n^{8} + 26488674632 n^{6} - 73130693640 n^{4} + 58597238304 n^{2} - 210416279040}{n^{2} \left(n^{32} - 537 n^{30} + 124020 n^{28} - 16232308 n^{26} + 1337335614 n^{24} - 72965083230 n^{22} + 2705859162420 n^{20} - 69038289172260 n^{18} + 1215300637100745 n^{16} - 14685432694210705 n^{14} + 120227485384616784 n^{12} - 652119798888556128 n^{10} + 2265918814119032320 n^{8} - 4808483584944152832 n^{6} + 5824456787792388096 n^{4} - 3654233298542592000 n^{2} + 917770131210240000\right)}\]
\[\operatorname{Wg}([4, 2, 2, 1, 1, 1, 1]) = \frac{- 5 n^{16} + 1461 n^{14} - 158559 n^{12} + 8320797 n^{10} - 236609772 n^{8} + 3637854978 n^{6} - 22866894964 n^{4} + 61849127664 n^{2} - 28979596800}{n^{3} \left(n^{30} - 521 n^{28} + 115684 n^{26} - 14381364 n^{24} + 1107233790 n^{22} - 55249342590 n^{20} + 1821869680980 n^{18} - 39888374276580 n^{16} + 577086648675465 n^{14} - 5452046315403265 n^{12} + 32994744338164544 n^{10} - 124203889477923424 n^{8} + 278656582472257536 n^{6} - 349978265388032256 n^{4} + 224804541583872000 n^{2} - 57360633200640000\right)}\]
\[\operatorname{Wg}([3, 3, 2, 1, 1, 1, 1]) = \frac{- 4 n^{10} + 764 n^{8} - 46332 n^{6} + 1596292 n^{4} - 31814864 n^{2} + 61698624}{n \left(n^{26} - 431 n^{24} + 76165 n^{22} - 7212315 n^{20} + 402601155 n^{18} - 13757461005 n^{16} + 290201948535 n^{14} - 3741009835785 n^{12} + 28838542972800 n^{10} - 129381277564000 n^{8} + 327131530233344 n^{6} - 443100412766464 n^{4} + 298659783168000 n^{2} - 78683996160000\right)}\]
\[\operatorname{Wg}([6, 2, 1, 1, 1, 1]) = \frac{42 n^{12} - 8172 n^{10} + 462054 n^{8} - 9633984 n^{6} + 69818364 n^{4} + 50027856 n^{2} + 46506240}{n^{2} \left(n^{28} - 447 n^{26} + 83061 n^{24} - 8430955 n^{22} + 517998195 n^{20} - 20199079485 n^{18} + 510321324615 n^{16} - 8384241012345 n^{14} + 88694700345360 n^{12} - 590797965128800 n^{10} + 2397231971257344 n^{8} - 5677204896499968 n^{6} + 7388266387431424 n^{4} - 4857240526848000 n^{2} + 1258943938560000\right)}\]
\[\operatorname{Wg}([5, 3, 1, 1, 1, 1]) = \frac{28 n^{16} - 6643 n^{14} + 452501 n^{12} - 2110311 n^{10} - 704415551 n^{8} + 21211246126 n^{6} - 217183319038 n^{4} + 770148182328 n^{2} - 774650701440}{n^{2} \left(n^{32} - 537 n^{30} + 124020 n^{28} - 16232308 n^{26} + 1337335614 n^{24} - 72965083230 n^{22} + 2705859162420 n^{20} - 69038289172260 n^{18} + 1215300637100745 n^{16} - 14685432694210705 n^{14} + 120227485384616784 n^{12} - 652119798888556128 n^{10} + 2265918814119032320 n^{8} - 4808483584944152832 n^{6} + 5824456787792388096 n^{4} - 3654233298542592000 n^{2} + 917770131210240000\right)}\]
\[\operatorname{Wg}([4, 4, 1, 1, 1, 1]) = \frac{25 n^{16} - 5435 n^{14} + 262457 n^{12} + 12639973 n^{10} - 1290136294 n^{8} + 32352994474 n^{6} - 301710018848 n^{4} + 934558613088 n^{2} - 462743677440}{n^{2} \left(n^{32} - 537 n^{30} + 124020 n^{28} - 16232308 n^{26} + 1337335614 n^{24} - 72965083230 n^{22} + 2705859162420 n^{20} - 69038289172260 n^{18} + 1215300637100745 n^{16} - 14685432694210705 n^{14} + 120227485384616784 n^{12} - 652119798888556128 n^{10} + 2265918814119032320 n^{8} - 4808483584944152832 n^{6} + 5824456787792388096 n^{4} - 3654233298542592000 n^{2} + 917770131210240000\right)}\]
\[\operatorname{Wg}([8, 1, 1, 1, 1]) = \frac{- 429 n^{12} + 114686 n^{10} - 10568987 n^{8} + 399818848 n^{6} - 5831428174 n^{4} + 26354475576 n^{2} - 17124307200}{n^{3} \left(n^{28} - 520 n^{26} + 115164 n^{24} - 14266200 n^{22} + 1092967590 n^{20} - 54156375000 n^{18} + 1767713305980 n^{16} - 38120660970600 n^{14} + 538965987704865 n^{12} - 4913080327698400 n^{10} + 28081664010466144 n^{8} - 96122225467457280 n^{6} + 182534357004800256 n^{4} - 167443908383232000 n^{2} + 57360633200640000\right)}\]
\[\operatorname{Wg}([3, 2, 2, 2, 1, 1, 1]) = \frac{- 2 n^{18} + 611 n^{16} - 74047 n^{14} + 4609599 n^{12} - 149181419 n^{10} + 1987401874 n^{8} + 1450078232 n^{6} - 222534410784 n^{4} + 906129870336 n^{2} - 284526950400}{n^{3} \left(n^{32} - 537 n^{30} + 124020 n^{28} - 16232308 n^{26} + 1337335614 n^{24} - 72965083230 n^{22} + 2705859162420 n^{20} - 69038289172260 n^{18} + 1215300637100745 n^{16} - 14685432694210705 n^{14} + 120227485384616784 n^{12} - 652119798888556128 n^{10} + 2265918814119032320 n^{8} - 4808483584944152832 n^{6} + 5824456787792388096 n^{4} - 3654233298542592000 n^{2} + 917770131210240000\right)}\]
\[\operatorname{Wg}([5, 2, 2, 1, 1, 1]) = \frac{14 n^{14} - 3426 n^{12} + 303838 n^{10} - 13292498 n^{8} + 323550372 n^{6} - 3260629396 n^{4} + 7568967576 n^{2} + 2087125920}{n^{2} \left(n^{30} - 521 n^{28} + 115684 n^{26} - 14381364 n^{24} + 1107233790 n^{22} - 55249342590 n^{20} + 1821869680980 n^{18} - 39888374276580 n^{16} + 577086648675465 n^{14} - 5452046315403265 n^{12} + 32994744338164544 n^{10} - 124203889477923424 n^{8} + 278656582472257536 n^{6} - 349978265388032256 n^{4} + 224804541583872000 n^{2} - 57360633200640000\right)}\]
\[\operatorname{Wg}([4, 3, 2, 1, 1, 1]) = \frac{10 n^{12} - 2169 n^{10} + 170536 n^{8} - 8431941 n^{6} + 343608124 n^{4} - 6485573040 n^{2} + 26607588480}{n^{2} \left(n^{28} - 520 n^{26} + 115164 n^{24} - 14266200 n^{22} + 1092967590 n^{20} - 54156375000 n^{18} + 1767713305980 n^{16} - 38120660970600 n^{14} + 538965987704865 n^{12} - 4913080327698400 n^{10} + 28081664010466144 n^{8} - 96122225467457280 n^{6} + 182534357004800256 n^{4} - 167443908383232000 n^{2} + 57360633200640000\right)}\]
\[\operatorname{Wg}([7, 2, 1, 1, 1]) = \frac{- 132 n^{14} + 31603 n^{12} - 2631794 n^{10} + 99345939 n^{8} - 2028923776 n^{6} + 23559594608 n^{4} - 130061403648 n^{2} + 216029721600}{n^{3} \left(n^{30} - 536 n^{28} + 123484 n^{26} - 16108824 n^{24} + 1321226790 n^{22} - 71643856440 n^{20} + 2634215305980 n^{18} - 66404073866280 n^{16} + 1148896563234465 n^{14} - 13536536130976240 n^{12} + 106690949253640544 n^{10} - 545428849634915584 n^{8} + 1720489964484116736 n^{6} - 3087993620460036096 n^{4} + 2736463167332352000 n^{2} - 917770131210240000\right)}\]
\[\operatorname{Wg}([3, 3, 3, 1, 1, 1]) = \frac{8 n^{16} - 1812 n^{14} + 175144 n^{12} - 13262042 n^{10} + 756424278 n^{8} - 21499847890 n^{6} + 252499343490 n^{4} - 1062922944456 n^{2} + 1132951121280}{n^{2} \left(n^{32} - 537 n^{30} + 124020 n^{28} - 16232308 n^{26} + 1337335614 n^{24} - 72965083230 n^{22} + 2705859162420 n^{20} - 69038289172260 n^{18} + 1215300637100745 n^{16} - 14685432694210705 n^{14} + 120227485384616784 n^{12} - 652119798888556128 n^{10} + 2265918814119032320 n^{8} - 4808483584944152832 n^{6} + 5824456787792388096 n^{4} - 3654233298542592000 n^{2} + 917770131210240000\right)}\]
\[\operatorname{Wg}([6, 3, 1, 1, 1]) = \frac{- 84 n^{16} + 14694 n^{14} - 389058 n^{12} - 40283382 n^{10} + 2147378718 n^{8} - 32842878168 n^{6} + 176803734624 n^{4} - 314197138944 n^{2} + 268719897600}{n^{3} \left(n^{32} - 537 n^{30} + 124020 n^{28} - 16232308 n^{26} + 1337335614 n^{24} - 72965083230 n^{22} + 2705859162420 n^{20} - 69038289172260 n^{18} + 1215300637100745 n^{16} - 14685432694210705 n^{14} + 120227485384616784 n^{12} - 652119798888556128 n^{10} + 2265918814119032320 n^{8} - 4808483584944152832 n^{6} + 5824456787792388096 n^{4} - 3654233298542592000 n^{2} + 917770131210240000\right)}\]
\[\operatorname{Wg}([5, 4, 1, 1, 1]) = \frac{- 70 n^{16} + 9198 n^{14} + 445942 n^{12} - 101962826 n^{10} + 4423825896 n^{8} - 71497345612 n^{6} + 420841020432 n^{4} - 675555068160 n^{2} + 221298739200}{n^{3} \left(n^{32} - 537 n^{30} + 124020 n^{28} - 16232308 n^{26} + 1337335614 n^{24} - 72965083230 n^{22} + 2705859162420 n^{20} - 69038289172260 n^{18} + 1215300637100745 n^{16} - 14685432694210705 n^{14} + 120227485384616784 n^{12} - 652119798888556128 n^{10} + 2265918814119032320 n^{8} - 4808483584944152832 n^{6} + 5824456787792388096 n^{4} - 3654233298542592000 n^{2} + 917770131210240000\right)}\]
\[\operatorname{Wg}([9, 1, 1, 1]) = \frac{1430 n^{8} - 303446 n^{6} + 19479460 n^{4} - 377993044 n^{2} + 657193680}{n^{2} \left(n^{26} - 511 n^{24} + 110565 n^{22} - 13271115 n^{20} + 973527555 n^{18} - 45394627005 n^{16} + 1359161662935 n^{14} - 25888206004185 n^{12} + 305972133667200 n^{10} - 2159331124693600 n^{8} + 8647683888223744 n^{6} - 18293070473443584 n^{4} + 17896722743808000 n^{2} - 6373403688960000\right)}\]
\[\operatorname{Wg}([2, 2, 2, 2, 2, 1, 1]) = \frac{- n^{14} + 195 n^{12} - 14599 n^{10} + 427525 n^{8} - 5491884 n^{6} + 41651740 n^{4} - 187047216 n^{2} - 526901760}{n^{3} \left(n^{28} - 421 n^{26} + 73584 n^{24} - 7022964 n^{22} + 404937390 n^{20} - 14755603590 n^{18} + 346309321980 n^{16} - 5257442078580 n^{14} + 51342440817465 n^{12} - 317802233656765 n^{10} + 1214520972488044 n^{8} - 2751792229119024 n^{6} + 3477359560355136 n^{4} - 2242309352518656 n^{2} + 573606332006400\right)}\]
\[\operatorname{Wg}([4, 2, 2, 2, 1, 1]) = \frac{5 n^{12} - 673 n^{10} + 42741 n^{8} - 879299 n^{6} - 1638062 n^{4} - 50741928 n^{2} + 188692416}{n^{2} \left(n^{28} - 421 n^{26} + 73584 n^{24} - 7022964 n^{22} + 404937390 n^{20} - 14755603590 n^{18} + 346309321980 n^{16} - 5257442078580 n^{14} + 51342440817465 n^{12} - 317802233656765 n^{10} + 1214520972488044 n^{8} - 2751792229119024 n^{6} + 3477359560355136 n^{4} - 2242309352518656 n^{2} + 573606332006400\right)}\]
\[\operatorname{Wg}([3, 3, 2, 2, 1, 1]) = \frac{4 n^{14} - 564 n^{12} + 43486 n^{10} - 1222606 n^{8} - 5884734 n^{6} + 421225754 n^{4} - 3366530556 n^{2} + 3968433216}{n^{2} \left(n^{30} - 437 n^{28} + 80320 n^{26} - 8200308 n^{24} + 517304814 n^{22} - 21234601830 n^{20} + 582398979420 n^{18} - 10798391230260 n^{16} + 135461514074745 n^{14} - 1139281286736205 n^{12} + 6299356710996284 n^{10} - 22184127788927728 n^{8} + 47506035226259520 n^{6} - 57880062318200832 n^{4} + 36450555972304896 n^{2} - 9177701312102400\right)}\]
\[\operatorname{Wg}([6, 2, 2, 1, 1]) = \frac{- 42 n^{12} + 3918 n^{10} - 187374 n^{8} + 3231354 n^{6} + 50798064 n^{4} - 226963872 n^{2} + 105380352}{n^{3} \left(n^{28} - 421 n^{26} + 73584 n^{24} - 7022964 n^{22} + 404937390 n^{20} - 14755603590 n^{18} + 346309321980 n^{16} - 5257442078580 n^{14} + 51342440817465 n^{12} - 317802233656765 n^{10} + 1214520972488044 n^{8} - 2751792229119024 n^{6} + 3477359560355136 n^{4} - 2242309352518656 n^{2} + 573606332006400\right)}\]
\[\operatorname{Wg}([5, 3, 2, 1, 1]) = \frac{- 28 n^{12} + 1795 n^{10} - 115254 n^{8} + 6509755 n^{6} - 100730668 n^{4} + 322344000 n^{2} + 1317254400}{n^{3} \left(n^{28} - 436 n^{26} + 79884 n^{24} - 8120424 n^{22} + 509184390 n^{20} - 20725417440 n^{18} + 561673561980 n^{16} - 10236717668280 n^{14} + 125224796406465 n^{12} - 1014056490329740 n^{10} + 5285300220666544 n^{8} - 16898827568261184 n^{6} + 30607207657998336 n^{4} - 27272854660202496 n^{2} + 9177701312102400\right)}\]
\[\operatorname{Wg}([4, 4, 2, 1, 1]) = \frac{- 25 n^{12} + 755 n^{10} - 68427 n^{8} + 6127825 n^{6} - 86346896 n^{4} + 321142320 n^{2} - 105380352}{n^{3} \left(n^{28} - 421 n^{26} + 73584 n^{24} - 7022964 n^{22} + 404937390 n^{20} - 14755603590 n^{18} + 346309321980 n^{16} - 5257442078580 n^{14} + 51342440817465 n^{12} - 317802233656765 n^{10} + 1214520972488044 n^{8} - 2751792229119024 n^{6} + 3477359560355136 n^{4} - 2242309352518656 n^{2} + 573606332006400\right)}\]
\[\operatorname{Wg}([8, 2, 1, 1]) = \frac{429 n^{6} - 29458 n^{4} + 896181 n^{2} - 23289552}{n^{2} \left(n^{24} - 416 n^{22} + 71500 n^{20} - 6663800 n^{18} + 371332390 n^{16} - 12872286440 n^{14} + 280462560220 n^{12} - 3803640131720 n^{10} + 31202389917985 n^{8} - 146575723539960 n^{6} + 356832795116304 n^{4} - 381325359377664 n^{2} + 143401583001600\right)}\]
\[\operatorname{Wg}([4, 3, 3, 1, 1]) = \frac{- 20 n^{14} + 892 n^{12} - 186174 n^{10} + 16759418 n^{8} - 410098342 n^{6} + 3286570338 n^{4} - 7251380064 n^{2} + 5374397952}{n^{3} \left(n^{30} - 437 n^{28} + 80320 n^{26} - 8200308 n^{24} + 517304814 n^{22} - 21234601830 n^{20} + 582398979420 n^{18} - 10798391230260 n^{16} + 135461514074745 n^{14} - 1139281286736205 n^{12} + 6299356710996284 n^{10} - 22184127788927728 n^{8} + 47506035226259520 n^{6} - 57880062318200832 n^{4} + 36450555972304896 n^{2} - 9177701312102400\right)}\]
\[\operatorname{Wg}([7, 3, 1, 1]) = \frac{264 n^{8} + 924 n^{6} - 942942 n^{4} + 6751866 n^{2} + 155520288}{n^{2} \left(n^{26} - 427 n^{24} + 76041 n^{22} - 7436055 n^{20} + 442259895 n^{18} - 16745078385 n^{16} + 410967856515 n^{14} - 6538006959645 n^{12} + 66382733769660 n^{10} - 416611886402800 n^{8} + 1535793243041344 n^{6} - 3076688380889088 n^{4} + 2917012229996544 n^{2} - 1019744590233600\right)}\]
\[\operatorname{Wg}([6, 4, 1, 1]) = \frac{210 n^{10} + 16530 n^{8} - 2094690 n^{6} + 37526790 n^{4} - 151371720 n^{2} + 48185280}{n^{2} \left(n^{28} - 421 n^{26} + 73584 n^{24} - 7022964 n^{22} + 404937390 n^{20} - 14755603590 n^{18} + 346309321980 n^{16} - 5257442078580 n^{14} + 51342440817465 n^{12} - 317802233656765 n^{10} + 1214520972488044 n^{8} - 2751792229119024 n^{6} + 3477359560355136 n^{4} - 2242309352518656 n^{2} + 573606332006400\right)}\]
\[\operatorname{Wg}([5, 5, 1, 1]) = \frac{196 n^{12} + 17444 n^{10} - 2827692 n^{8} + 93401252 n^{6} - 1190341544 n^{4} + 5182876104 n^{2} - 6115253760}{n^{2} \left(n^{30} - 437 n^{28} + 80320 n^{26} - 8200308 n^{24} + 517304814 n^{22} - 21234601830 n^{20} + 582398979420 n^{18} - 10798391230260 n^{16} + 135461514074745 n^{14} - 1139281286736205 n^{12} + 6299356710996284 n^{10} - 22184127788927728 n^{8} + 47506035226259520 n^{6} - 57880062318200832 n^{4} + 36450555972304896 n^{2} - 9177701312102400\right)}\]
\[\operatorname{Wg}([10, 1, 1]) = \frac{- 4862 n^{2} + 252382}{n \left(n^{22} - 407 n^{20} + 67837 n^{18} - 6053267 n^{16} + 316852987 n^{14} - 10020609557 n^{12} + 190277074207 n^{10} - 2091146463857 n^{8} + 12382071743272 n^{6} - 35137077850512 n^{4} + 40599094461696 n^{2} - 15933509222400\right)}\]
\[\operatorname{Wg}([3, 2, 2, 2, 2, 1]) = \frac{2 n^{16} - 505 n^{14} + 55247 n^{12} - 2833943 n^{10} + 71395615 n^{8} - 1271085044 n^{6} - 21156760284 n^{4} + 502080471792 n^{2} - 680901914880}{n^{2} \left(n^{32} - 537 n^{30} + 124020 n^{28} - 16232308 n^{26} + 1337335614 n^{24} - 72965083230 n^{22} + 2705859162420 n^{20} - 69038289172260 n^{18} + 1215300637100745 n^{16} - 14685432694210705 n^{14} + 120227485384616784 n^{12} - 652119798888556128 n^{10} + 2265918814119032320 n^{8} - 4808483584944152832 n^{6} + 5824456787792388096 n^{4} - 3654233298542592000 n^{2} + 917770131210240000\right)}\]
\[\operatorname{Wg}([5, 2, 2, 2, 1]) = \frac{- 14 n^{16} + 2682 n^{14} - 241890 n^{12} + 10323286 n^{10} - 163462248 n^{8} + 6573943752 n^{6} - 92964842048 n^{4} + 188092615680 n^{2} + 200222668800}{n^{3} \left(n^{32} - 537 n^{30} + 124020 n^{28} - 16232308 n^{26} + 1337335614 n^{24} - 72965083230 n^{22} + 2705859162420 n^{20} - 69038289172260 n^{18} + 1215300637100745 n^{16} - 14685432694210705 n^{14} + 120227485384616784 n^{12} - 652119798888556128 n^{10} + 2265918814119032320 n^{8} - 4808483584944152832 n^{6} + 5824456787792388096 n^{4} - 3654233298542592000 n^{2} + 917770131210240000\right)}\]
\[\operatorname{Wg}([4, 3, 2, 2, 1]) = \frac{- 10 n^{14} + 1513 n^{12} - 137497 n^{10} + 5280409 n^{8} + 67473839 n^{6} + 1503881578 n^{4} - 2654253432 n^{2} + 14489798400}{n^{3} \left(n^{30} - 521 n^{28} + 115684 n^{26} - 14381364 n^{24} + 1107233790 n^{22} - 55249342590 n^{20} + 1821869680980 n^{18} - 39888374276580 n^{16} + 577086648675465 n^{14} - 5452046315403265 n^{12} + 32994744338164544 n^{10} - 124203889477923424 n^{8} + 278656582472257536 n^{6} - 349978265388032256 n^{4} + 224804541583872000 n^{2} - 57360633200640000\right)}\]
\[\operatorname{Wg}([7, 2, 2, 1]) = \frac{132 n^{12} - 20009 n^{10} + 1420716 n^{8} - 50435517 n^{6} - 430304578 n^{4} + 22542685176 n^{2} - 143709793920}{n^{2} \left(n^{30} - 536 n^{28} + 123484 n^{26} - 16108824 n^{24} + 1321226790 n^{22} - 71643856440 n^{20} + 2634215305980 n^{18} - 66404073866280 n^{16} + 1148896563234465 n^{14} - 13536536130976240 n^{12} + 106690949253640544 n^{10} - 545428849634915584 n^{8} + 1720489964484116736 n^{6} - 3087993620460036096 n^{4} + 2736463167332352000 n^{2} - 917770131210240000\right)}\]
\[\operatorname{Wg}([3, 3, 3, 2, 1]) = \frac{- 8 n^{12} + 572 n^{10} - 89292 n^{8} - 1794136 n^{6} + 75612160 n^{4} + 202639104 n^{2} + 195148800}{n^{3} \left(n^{28} - 447 n^{26} + 83061 n^{24} - 8430955 n^{22} + 517998195 n^{20} - 20199079485 n^{18} + 510321324615 n^{16} - 8384241012345 n^{14} + 88694700345360 n^{12} - 590797965128800 n^{10} + 2397231971257344 n^{8} - 5677204896499968 n^{6} + 7388266387431424 n^{4} - 4857240526848000 n^{2} + 1258943938560000\right)}\]
\[\operatorname{Wg}([6, 3, 2, 1]) = \frac{84 n^{10} - 54 n^{8} + 387816 n^{6} + 2129874 n^{4} - 214079400 n^{2} + 368734080}{n^{2} \left(n^{28} - 447 n^{26} + 83061 n^{24} - 8430955 n^{22} + 517998195 n^{20} - 20199079485 n^{18} + 510321324615 n^{16} - 8384241012345 n^{14} + 88694700345360 n^{12} - 590797965128800 n^{10} + 2397231971257344 n^{8} - 5677204896499968 n^{6} + 7388266387431424 n^{4} - 4857240526848000 n^{2} + 1258943938560000\right)}\]
\[\operatorname{Wg}([5, 4, 2, 1]) = \frac{70 n^{10} + 3384 n^{8} + 304734 n^{6} - 3119644 n^{4} + 128369856 n^{2} - 209383680}{n^{2} \left(n^{28} - 440 n^{26} + 80044 n^{24} - 7897800 n^{22} + 467511990 n^{20} - 17380871400 n^{18} + 414019097580 n^{16} - 6352827372600 n^{14} + 62507631494865 n^{12} - 388928164319200 n^{10} + 1491563028309344 n^{8} - 3387284184866560 n^{6} + 4286563498066176 n^{4} - 2766622044672000 n^{2} + 708155965440000\right)}\]
\[\operatorname{Wg}([9, 2, 1]) = \frac{- 1430 n^{4} + 33592 n^{2} - 3761888}{n \left(n^{24} - 430 n^{22} + 75735 n^{20} - 7136580 n^{18} + 395464575 n^{16} - 13361996430 n^{14} + 276839952105 n^{12} - 3464169883680 n^{10} + 25374373089120 n^{8} - 104006904474880 n^{6} + 223124625758464 n^{4} - 219975787008000 n^{2} + 78683996160000\right)}\]
\[\operatorname{Wg}([5, 3, 3, 1]) = \frac{56 n^{14} - 3052 n^{12} + 693854 n^{10} - 105102746 n^{8} + 3465131194 n^{6} - 33462730322 n^{4} + 74826124296 n^{2} - 245904785280}{n^{2} \left(n^{32} - 537 n^{30} + 124020 n^{28} - 16232308 n^{26} + 1337335614 n^{24} - 72965083230 n^{22} + 2705859162420 n^{20} - 69038289172260 n^{18} + 1215300637100745 n^{16} - 14685432694210705 n^{14} + 120227485384616784 n^{12} - 652119798888556128 n^{10} + 2265918814119032320 n^{8} - 4808483584944152832 n^{6} + 5824456787792388096 n^{4} - 3654233298542592000 n^{2} + 917770131210240000\right)}\]
\[\operatorname{Wg}([4, 4, 3, 1]) = \frac{50 n^{14} - 1905 n^{12} + 748015 n^{10} - 129438275 n^{8} + 5176485075 n^{6} - 71989204240 n^{4} + 260831754960 n^{2} + 7290328320}{n^{2} \left(n^{32} - 537 n^{30} + 124020 n^{28} - 16232308 n^{26} + 1337335614 n^{24} - 72965083230 n^{22} + 2705859162420 n^{20} - 69038289172260 n^{18} + 1215300637100745 n^{16} - 14685432694210705 n^{14} + 120227485384616784 n^{12} - 652119798888556128 n^{10} + 2265918814119032320 n^{8} - 4808483584944152832 n^{6} + 5824456787792388096 n^{4} - 3654233298542592000 n^{2} + 917770131210240000\right)}\]
\[\operatorname{Wg}([8, 3, 1]) = \frac{- 858 n^{10} + 11635 n^{8} + 4287556 n^{6} + 106678975 n^{4} - 4885026588 n^{2} + 8562153600}{n^{3} \left(n^{28} - 520 n^{26} + 115164 n^{24} - 14266200 n^{22} + 1092967590 n^{20} - 54156375000 n^{18} + 1767713305980 n^{16} - 38120660970600 n^{14} + 538965987704865 n^{12} - 4913080327698400 n^{10} + 28081664010466144 n^{8} - 96122225467457280 n^{6} + 182534357004800256 n^{4} - 167443908383232000 n^{2} + 57360633200640000\right)}\]
\[\operatorname{Wg}([7, 4, 1]) = \frac{- 660 n^{12} - 43707 n^{10} + 12923910 n^{8} - 458763891 n^{6} + 4920325500 n^{4} + 9197062848 n^{2} - 216029721600}{n^{3} \left(n^{30} - 536 n^{28} + 123484 n^{26} - 16108824 n^{24} + 1321226790 n^{22} - 71643856440 n^{20} + 2634215305980 n^{18} - 66404073866280 n^{16} + 1148896563234465 n^{14} - 13536536130976240 n^{12} + 106690949253640544 n^{10} - 545428849634915584 n^{8} + 1720489964484116736 n^{6} - 3087993620460036096 n^{4} + 2736463167332352000 n^{2} - 917770131210240000\right)}\]
\[\operatorname{Wg}([6, 5, 1]) = \frac{- 588 n^{12} - 72240 n^{10} + 17282916 n^{8} - 778482600 n^{6} + 16209396672 n^{4} - 153919503360 n^{2} + 353024179200}{n^{3} \left(n^{30} - 536 n^{28} + 123484 n^{26} - 16108824 n^{24} + 1321226790 n^{22} - 71643856440 n^{20} + 2634215305980 n^{18} - 66404073866280 n^{16} + 1148896563234465 n^{14} - 13536536130976240 n^{12} + 106690949253640544 n^{10} - 545428849634915584 n^{8} + 1720489964484116736 n^{6} - 3087993620460036096 n^{4} + 2736463167332352000 n^{2} - 917770131210240000\right)}\]
\[\operatorname{Wg}([11, 1]) = \frac{16796 n^{2} - 1385670}{n^{2} \left(n^{22} - 506 n^{20} + 108031 n^{18} - 12728936 n^{16} + 909450751 n^{14} - 40796457506 n^{12} + 1151541572401 n^{10} - 19967312312156 n^{8} + 201529405816816 n^{6} - 1071814846360896 n^{4} + 2482492033152000 n^{2} - 1593350922240000\right)}\]
\[\operatorname{Wg}([2, 2, 2, 2, 2, 2]) = \frac{n^{16} - 261 n^{14} + 29469 n^{12} - 1463459 n^{10} + 49398534 n^{8} + 104425116 n^{6} + 52040291656 n^{4} - 747928819296 n^{2} + 3713446218240}{n^{2} \left(n^{32} - 537 n^{30} + 124020 n^{28} - 16232308 n^{26} + 1337335614 n^{24} - 72965083230 n^{22} + 2705859162420 n^{20} - 69038289172260 n^{18} + 1215300637100745 n^{16} - 14685432694210705 n^{14} + 120227485384616784 n^{12} - 652119798888556128 n^{10} + 2265918814119032320 n^{8} - 4808483584944152832 n^{6} + 5824456787792388096 n^{4} - 3654233298542592000 n^{2} + 917770131210240000\right)}\]
\[\operatorname{Wg}([4, 2, 2, 2, 2]) = \frac{- 5 n^{16} + 935 n^{14} - 96955 n^{12} + 2904465 n^{10} - 146717540 n^{8} - 3823462820 n^{6} + 66011546000 n^{4} - 347529127680 n^{2} + 84304281600}{n^{3} \left(n^{32} - 537 n^{30} + 124020 n^{28} - 16232308 n^{26} + 1337335614 n^{24} - 72965083230 n^{22} + 2705859162420 n^{20} - 69038289172260 n^{18} + 1215300637100745 n^{16} - 14685432694210705 n^{14} + 120227485384616784 n^{12} - 652119798888556128 n^{10} + 2265918814119032320 n^{8} - 4808483584944152832 n^{6} + 5824456787792388096 n^{4} - 3654233298542592000 n^{2} + 917770131210240000\right)}\]
\[\operatorname{Wg}([3, 3, 2, 2, 2]) = \frac{- 4 n^{16} + 716 n^{14} - 79756 n^{12} + 1933780 n^{10} - 123853856 n^{8} - 2560950128 n^{6} + 159646617216 n^{4} - 1131252922368 n^{2} + 1074879590400}{n^{3} \left(n^{32} - 537 n^{30} + 124020 n^{28} - 16232308 n^{26} + 1337335614 n^{24} - 72965083230 n^{22} + 2705859162420 n^{20} - 69038289172260 n^{18} + 1215300637100745 n^{16} - 14685432694210705 n^{14} + 120227485384616784 n^{12} - 652119798888556128 n^{10} + 2265918814119032320 n^{8} - 4808483584944152832 n^{6} + 5824456787792388096 n^{4} - 3654233298542592000 n^{2} + 917770131210240000\right)}\]
\[\operatorname{Wg}([6, 2, 2, 2]) = \frac{42 n^{14} - 5376 n^{12} + 528360 n^{10} - 5684028 n^{8} + 782650974 n^{6} - 9467289636 n^{4} + 11412125424 n^{2} - 304493333760}{n^{2} \left(n^{32} - 537 n^{30} + 124020 n^{28} - 16232308 n^{26} + 1337335614 n^{24} - 72965083230 n^{22} + 2705859162420 n^{20} - 69038289172260 n^{18} + 1215300637100745 n^{16} - 14685432694210705 n^{14} + 120227485384616784 n^{12} - 652119798888556128 n^{10} + 2265918814119032320 n^{8} - 4808483584944152832 n^{6} + 5824456787792388096 n^{4} - 3654233298542592000 n^{2} + 917770131210240000\right)}\]
\[\operatorname{Wg}([5, 3, 2, 2]) = \frac{28 n^{14} - 2435 n^{12} + 358171 n^{10} - 314215 n^{8} + 459194549 n^{6} - 14821871290 n^{4} + 15475933752 n^{2} + 200067373440}{n^{2} \left(n^{32} - 537 n^{30} + 124020 n^{28} - 16232308 n^{26} + 1337335614 n^{24} - 72965083230 n^{22} + 2705859162420 n^{20} - 69038289172260 n^{18} + 1215300637100745 n^{16} - 14685432694210705 n^{14} + 120227485384616784 n^{12} - 652119798888556128 n^{10} + 2265918814119032320 n^{8} - 4808483584944152832 n^{6} + 5824456787792388096 n^{4} - 3654233298542592000 n^{2} + 917770131210240000\right)}\]
\[\operatorname{Wg}([4, 4, 2, 2]) = \frac{25 n^{14} - 1725 n^{12} + 316025 n^{10} + 117905 n^{8} + 326744010 n^{6} - 5266040720 n^{4} + 67492671840 n^{2} + 138626864640}{n^{2} \left(n^{32} - 537 n^{30} + 124020 n^{28} - 16232308 n^{26} + 1337335614 n^{24} - 72965083230 n^{22} + 2705859162420 n^{20} - 69038289172260 n^{18} + 1215300637100745 n^{16} - 14685432694210705 n^{14} + 120227485384616784 n^{12} - 652119798888556128 n^{10} + 2265918814119032320 n^{8} - 4808483584944152832 n^{6} + 5824456787792388096 n^{4} - 3654233298542592000 n^{2} + 917770131210240000\right)}\]
\[\operatorname{Wg}([8, 2, 2]) = \frac{- 429 n^{10} + 30888 n^{8} - 3252249 n^{6} - 62188698 n^{4} + 82707768 n^{2} - 17124307200}{n^{3} \left(n^{28} - 520 n^{26} + 115164 n^{24} - 14266200 n^{22} + 1092967590 n^{20} - 54156375000 n^{18} + 1767713305980 n^{16} - 38120660970600 n^{14} + 538965987704865 n^{12} - 4913080327698400 n^{10} + 28081664010466144 n^{8} - 96122225467457280 n^{6} + 182534357004800256 n^{4} - 167443908383232000 n^{2} + 57360633200640000\right)}\]
\[\operatorname{Wg}([4, 3, 3, 2]) = \frac{20 n^{12} - 1060 n^{10} + 355140 n^{8} + 8023060 n^{6} - 172610120 n^{4} - 9068332800 n^{2} + 29350632960}{n^{2} \left(n^{30} - 521 n^{28} + 115684 n^{26} - 14381364 n^{24} + 1107233790 n^{22} - 55249342590 n^{20} + 1821869680980 n^{18} - 39888374276580 n^{16} + 577086648675465 n^{14} - 5452046315403265 n^{12} + 32994744338164544 n^{10} - 124203889477923424 n^{8} + 278656582472257536 n^{6} - 349978265388032256 n^{4} + 224804541583872000 n^{2} - 57360633200640000\right)}\]
\[\operatorname{Wg}([7, 3, 2]) = \frac{- 264 n^{12} + 2288 n^{10} - 1788072 n^{8} - 41348736 n^{6} + 3916534336 n^{4} - 51773559552 n^{2} + 216029721600}{n^{3} \left(n^{30} - 536 n^{28} + 123484 n^{26} - 16108824 n^{24} + 1321226790 n^{22} - 71643856440 n^{20} + 2634215305980 n^{18} - 66404073866280 n^{16} + 1148896563234465 n^{14} - 13536536130976240 n^{12} + 106690949253640544 n^{10} - 545428849634915584 n^{8} + 1720489964484116736 n^{6} - 3087993620460036096 n^{4} + 2736463167332352000 n^{2} - 917770131210240000\right)}\]
\[\operatorname{Wg}([6, 4, 2]) = \frac{- 210 n^{14} - 12096 n^{12} - 711564 n^{10} - 30094008 n^{8} + 972346158 n^{6} - 492516696 n^{4} - 268689907584 n^{2} + 368831232000}{n^{3} \left(n^{32} - 537 n^{30} + 124020 n^{28} - 16232308 n^{26} + 1337335614 n^{24} - 72965083230 n^{22} + 2705859162420 n^{20} - 69038289172260 n^{18} + 1215300637100745 n^{16} - 14685432694210705 n^{14} + 120227485384616784 n^{12} - 652119798888556128 n^{10} + 2265918814119032320 n^{8} - 4808483584944152832 n^{6} + 5824456787792388096 n^{4} - 3654233298542592000 n^{2} + 917770131210240000\right)}\]
\[\operatorname{Wg}([5, 5, 2]) = \frac{- 196 n^{14} - 16324 n^{12} - 352828 n^{10} - 25059692 n^{8} - 941353616 n^{6} + 67020135616 n^{4} - 509608834560 n^{2} + 242374809600}{n^{3} \left(n^{32} - 537 n^{30} + 124020 n^{28} - 16232308 n^{26} + 1337335614 n^{24} - 72965083230 n^{22} + 2705859162420 n^{20} - 69038289172260 n^{18} + 1215300637100745 n^{16} - 14685432694210705 n^{14} + 120227485384616784 n^{12} - 652119798888556128 n^{10} + 2265918814119032320 n^{8} - 4808483584944152832 n^{6} + 5824456787792388096 n^{4} - 3654233298542592000 n^{2} + 917770131210240000\right)}\]
\[\operatorname{Wg}([10, 2]) = \frac{4862 n^{4} - 150722 n^{2} + 24650340}{n^{2} \left(n^{24} - 507 n^{22} + 108537 n^{20} - 12836967 n^{18} + 922179687 n^{16} - 41705908257 n^{14} + 1192338029907 n^{12} - 21118853884557 n^{10} + 221496718128972 n^{8} - 1273344252177712 n^{6} + 3554306879512896 n^{4} - 4075842955392000 n^{2} + 1593350922240000\right)}\]
\[\operatorname{Wg}([3, 3, 3, 3]) = \frac{16 n^{14} - 1072 n^{12} + 358224 n^{10} + 17509904 n^{8} - 1775952416 n^{6} + 11586335328 n^{4} + 259327310976 n^{2} + 937928471040}{n^{2} \left(n^{32} - 537 n^{30} + 124020 n^{28} - 16232308 n^{26} + 1337335614 n^{24} - 72965083230 n^{22} + 2705859162420 n^{20} - 69038289172260 n^{18} + 1215300637100745 n^{16} - 14685432694210705 n^{14} + 120227485384616784 n^{12} - 652119798888556128 n^{10} + 2265918814119032320 n^{8} - 4808483584944152832 n^{6} + 5824456787792388096 n^{4} - 3654233298542592000 n^{2} + 917770131210240000\right)}\]
\[\operatorname{Wg}([6, 3, 3]) = \frac{- 168 n^{14} - 7224 n^{12} - 3425352 n^{10} + 159107928 n^{8} + 470491728 n^{6} - 37053899904 n^{4} - 133138833408 n^{2} - 31614105600}{n^{3} \left(n^{32} - 537 n^{30} + 124020 n^{28} - 16232308 n^{26} + 1337335614 n^{24} - 72965083230 n^{22} + 2705859162420 n^{20} - 69038289172260 n^{18} + 1215300637100745 n^{16} - 14685432694210705 n^{14} + 120227485384616784 n^{12} - 652119798888556128 n^{10} + 2265918814119032320 n^{8} - 4808483584944152832 n^{6} + 5824456787792388096 n^{4} - 3654233298542592000 n^{2} + 917770131210240000\right)}\]
\[\operatorname{Wg}([5, 4, 3]) = \frac{- 140 n^{14} - 11305 n^{12} - 4002705 n^{10} + 291764585 n^{8} - 6645300095 n^{6} + 51613342620 n^{4} + 45275509440 n^{2} + 110649369600}{n^{3} \left(n^{32} - 537 n^{30} + 124020 n^{28} - 16232308 n^{26} + 1337335614 n^{24} - 72965083230 n^{22} + 2705859162420 n^{20} - 69038289172260 n^{18} + 1215300637100745 n^{16} - 14685432694210705 n^{14} + 120227485384616784 n^{12} - 652119798888556128 n^{10} + 2265918814119032320 n^{8} - 4808483584944152832 n^{6} + 5824456787792388096 n^{4} - 3654233298542592000 n^{2} + 917770131210240000\right)}\]
\[\operatorname{Wg}([9, 3]) = \frac{2860 n^{6} + 230230 n^{4} + 10320310 n^{2} - 607309560}{n^{2} \left(n^{26} - 511 n^{24} + 110565 n^{22} - 13271115 n^{20} + 973527555 n^{18} - 45394627005 n^{16} + 1359161662935 n^{14} - 25888206004185 n^{12} + 305972133667200 n^{10} - 2159331124693600 n^{8} + 8647683888223744 n^{6} - 18293070473443584 n^{4} + 17896722743808000 n^{2} - 6373403688960000\right)}\]
\[\operatorname{Wg}([4, 4, 4]) = \frac{- 125 n^{12} - 13625 n^{10} - 5067375 n^{8} + 329254925 n^{6} - 6059236600 n^{4} - 40967593200 n^{2} + 86938790400}{n^{3} \left(n^{30} - 521 n^{28} + 115684 n^{26} - 14381364 n^{24} + 1107233790 n^{22} - 55249342590 n^{20} + 1821869680980 n^{18} - 39888374276580 n^{16} + 577086648675465 n^{14} - 5452046315403265 n^{12} + 32994744338164544 n^{10} - 124203889477923424 n^{8} + 278656582472257536 n^{6} - 349978265388032256 n^{4} + 224804541583872000 n^{2} - 57360633200640000\right)}\]
\[\operatorname{Wg}([8, 4]) = \frac{2145 n^{8} + 416130 n^{6} - 11906895 n^{4} - 128125140 n^{2} + 9670415040}{n^{2} \left(n^{28} - 520 n^{26} + 115164 n^{24} - 14266200 n^{22} + 1092967590 n^{20} - 54156375000 n^{18} + 1767713305980 n^{16} - 38120660970600 n^{14} + 538965987704865 n^{12} - 4913080327698400 n^{10} + 28081664010466144 n^{8} - 96122225467457280 n^{6} + 182534357004800256 n^{4} - 167443908383232000 n^{2} + 57360633200640000\right)}\]
\[\operatorname{Wg}([7, 5]) = \frac{1848 n^{10} + 494340 n^{8} - 34616736 n^{6} + 1112565300 n^{4} - 18011151312 n^{2} + 85390018560}{n^{2} \left(n^{30} - 536 n^{28} + 123484 n^{26} - 16108824 n^{24} + 1321226790 n^{22} - 71643856440 n^{20} + 2634215305980 n^{18} - 66404073866280 n^{16} + 1148896563234465 n^{14} - 13536536130976240 n^{12} + 106690949253640544 n^{10} - 545428849634915584 n^{8} + 1720489964484116736 n^{6} - 3087993620460036096 n^{4} + 2736463167332352000 n^{2} - 917770131210240000\right)}\]
\[\operatorname{Wg}([6, 6]) = \frac{1764 n^{10} + 529200 n^{8} - 40266828 n^{6} + 1559217240 n^{4} - 35217243936 n^{2} + 343571880960}{n^{2} \left(n^{30} - 536 n^{28} + 123484 n^{26} - 16108824 n^{24} + 1321226790 n^{22} - 71643856440 n^{20} + 2634215305980 n^{18} - 66404073866280 n^{16} + 1148896563234465 n^{14} - 13536536130976240 n^{12} + 106690949253640544 n^{10} - 545428849634915584 n^{8} + 1720489964484116736 n^{6} - 3087993620460036096 n^{4} + 2736463167332352000 n^{2} - 917770131210240000\right)}\]
\[\operatorname{Wg}([12]) = - \frac{58786}{n \left(n^{22} - 506 n^{20} + 108031 n^{18} - 12728936 n^{16} + 909450751 n^{14} - 40796457506 n^{12} + 1151541572401 n^{10} - 19967312312156 n^{8} + 201529405816816 n^{6} - 1071814846360896 n^{4} + 2482492033152000 n^{2} - 1593350922240000\right)}\]