Weingarten functions for p = 11
Below are the values of the Weingarten function for permutation size p = 11. The input is given as a partition of p. You can also download them as a text file or as a python pickle file.
\[\operatorname{Wg}([1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]) = \frac{n^{18} - 344 n^{16} + 47305 n^{14} - 3338030 n^{12} + 129218848 n^{10} - 2728819832 n^{8} + 29688278076 n^{6} - 149061471624 n^{4} + 273312649440 n^{2} - 38799129600}{n^{3} \left(n^{26} - 399 n^{24} + 66885 n^{22} - 6173115 n^{20} + 346020675 n^{18} - 12287873325 n^{16} + 280880633655 n^{14} - 4134104298345 n^{12} + 38739367605120 n^{10} - 225616847478880 n^{8} + 782025465521664 n^{6} - 1497144139335936 n^{4} + 1379916145152000 n^{2} - 474054819840000\right)}\]
\[\operatorname{Wg}([2, 1, 1, 1, 1, 1, 1, 1, 1, 1]) = \frac{- n^{16} + 326 n^{14} - 41797 n^{12} + 2688500 n^{10} - 91884112 n^{8} + 1635300968 n^{6} - 13995701820 n^{4} + 49708341936 n^{2} - 48846551040}{n^{2} \left(n^{26} - 399 n^{24} + 66885 n^{22} - 6173115 n^{20} + 346020675 n^{18} - 12287873325 n^{16} + 280880633655 n^{14} - 4134104298345 n^{12} + 38739367605120 n^{10} - 225616847478880 n^{8} + 782025465521664 n^{6} - 1497144139335936 n^{4} + 1379916145152000 n^{2} - 474054819840000\right)}\]
\[\operatorname{Wg}([3, 1, 1, 1, 1, 1, 1, 1, 1]) = \frac{2 n^{16} - 612 n^{14} + 72170 n^{12} - 4148304 n^{10} + 121502096 n^{8} - 1743619584 n^{6} + 11039236632 n^{4} - 24940677600 n^{2} + 4311014400}{n^{3} \left(n^{26} - 399 n^{24} + 66885 n^{22} - 6173115 n^{20} + 346020675 n^{18} - 12287873325 n^{16} + 280880633655 n^{14} - 4134104298345 n^{12} + 38739367605120 n^{10} - 225616847478880 n^{8} + 782025465521664 n^{6} - 1497144139335936 n^{4} + 1379916145152000 n^{2} - 474054819840000\right)}\]
\[\operatorname{Wg}([2, 2, 1, 1, 1, 1, 1, 1, 1]) = \frac{n^{16} - 302 n^{14} + 35119 n^{12} - 1992224 n^{10} + 57820486 n^{8} - 828604784 n^{6} + 5240619624 n^{4} - 11643104160 n^{2} + 6923750400}{n^{3} \left(n^{26} - 399 n^{24} + 66885 n^{22} - 6173115 n^{20} + 346020675 n^{18} - 12287873325 n^{16} + 280880633655 n^{14} - 4134104298345 n^{12} + 38739367605120 n^{10} - 225616847478880 n^{8} + 782025465521664 n^{6} - 1497144139335936 n^{4} + 1379916145152000 n^{2} - 474054819840000\right)}\]
\[\operatorname{Wg}([4, 1, 1, 1, 1, 1, 1, 1]) = \frac{- 5 n^{14} + 1428 n^{12} - 153587 n^{10} + 7783266 n^{8} - 190872794 n^{6} + 2119020876 n^{4} - 9309500784 n^{2} + 11672760960}{n^{2} \left(n^{26} - 399 n^{24} + 66885 n^{22} - 6173115 n^{20} + 346020675 n^{18} - 12287873325 n^{16} + 280880633655 n^{14} - 4134104298345 n^{12} + 38739367605120 n^{10} - 225616847478880 n^{8} + 782025465521664 n^{6} - 1497144139335936 n^{4} + 1379916145152000 n^{2} - 474054819840000\right)}\]
\[\operatorname{Wg}([3, 2, 1, 1, 1, 1, 1, 1]) = \frac{- 2 n^{12} + 528 n^{10} - 50834 n^{8} + 2184936 n^{6} - 41042804 n^{4} + 275906256 n^{2} - 294877440}{n^{2} \left(n^{24} - 390 n^{22} + 63375 n^{20} - 5602740 n^{18} + 295596015 n^{16} - 9627509190 n^{14} + 194233050945 n^{12} - 2386006839840 n^{10} + 17265306046560 n^{8} - 70229093059840 n^{6} + 149963627983104 n^{4} - 147471487488000 n^{2} + 52672757760000\right)}\]
\[\operatorname{Wg}([5, 1, 1, 1, 1, 1, 1]) = \frac{14 n^{14} - 3696 n^{12} + 357938 n^{10} - 15707412 n^{8} + 313831868 n^{6} - 2572798872 n^{4} + 7121671200 n^{2} - 2220825600}{n^{3} \left(n^{26} - 399 n^{24} + 66885 n^{22} - 6173115 n^{20} + 346020675 n^{18} - 12287873325 n^{16} + 280880633655 n^{14} - 4134104298345 n^{12} + 38739367605120 n^{10} - 225616847478880 n^{8} + 782025465521664 n^{6} - 1497144139335936 n^{4} + 1379916145152000 n^{2} - 474054819840000\right)}\]
\[\operatorname{Wg}([2, 2, 2, 1, 1, 1, 1, 1]) = \frac{- n^{14} + 272 n^{12} - 27939 n^{10} + 1373134 n^{8} - 33834566 n^{6} + 392961564 n^{4} - 1655003664 n^{2} + 1788168960}{n^{2} \left(n^{26} - 399 n^{24} + 66885 n^{22} - 6173115 n^{20} + 346020675 n^{18} - 12287873325 n^{16} + 280880633655 n^{14} - 4134104298345 n^{12} + 38739367605120 n^{10} - 225616847478880 n^{8} + 782025465521664 n^{6} - 1497144139335936 n^{4} + 1379916145152000 n^{2} - 474054819840000\right)}\]
\[\operatorname{Wg}([4, 2, 1, 1, 1, 1, 1]) = \frac{5 n^{12} - 1165 n^{10} + 93870 n^{8} - 3074990 n^{6} + 36367480 n^{4} - 98960640 n^{2} + 174182400}{n^{3} \left(n^{24} - 390 n^{22} + 63375 n^{20} - 5602740 n^{18} + 295596015 n^{16} - 9627509190 n^{14} + 194233050945 n^{12} - 2386006839840 n^{10} + 17265306046560 n^{8} - 70229093059840 n^{6} + 149963627983104 n^{4} - 147471487488000 n^{2} + 52672757760000\right)}\]
\[\operatorname{Wg}([3, 3, 1, 1, 1, 1, 1]) = \frac{4 n^{14} - 916 n^{12} + 72008 n^{10} - 2278772 n^{8} + 26138748 n^{6} - 90467712 n^{4} + 153627840 n^{2} + 391910400}{n^{3} \left(n^{26} - 399 n^{24} + 66885 n^{22} - 6173115 n^{20} + 346020675 n^{18} - 12287873325 n^{16} + 280880633655 n^{14} - 4134104298345 n^{12} + 38739367605120 n^{10} - 225616847478880 n^{8} + 782025465521664 n^{6} - 1497144139335936 n^{4} + 1379916145152000 n^{2} - 474054819840000\right)}\]
\[\operatorname{Wg}([6, 1, 1, 1, 1, 1]) = \frac{- 42 n^{12} + 10068 n^{10} - 857334 n^{8} + 31554696 n^{6} - 492637644 n^{4} + 2842232976 n^{2} - 4405415040}{n^{2} \left(n^{26} - 399 n^{24} + 66885 n^{22} - 6173115 n^{20} + 346020675 n^{18} - 12287873325 n^{16} + 280880633655 n^{14} - 4134104298345 n^{12} + 38739367605120 n^{10} - 225616847478880 n^{8} + 782025465521664 n^{6} - 1497144139335936 n^{4} + 1379916145152000 n^{2} - 474054819840000\right)}\]
\[\operatorname{Wg}([3, 2, 2, 1, 1, 1, 1]) = \frac{2 n^{14} - 468 n^{12} + 40334 n^{10} - 1661328 n^{8} + 35894732 n^{6} - 376108824 n^{4} + 1119124512 n^{2} - 130636800}{n^{3} \left(n^{26} - 399 n^{24} + 66885 n^{22} - 6173115 n^{20} + 346020675 n^{18} - 12287873325 n^{16} + 280880633655 n^{14} - 4134104298345 n^{12} + 38739367605120 n^{10} - 225616847478880 n^{8} + 782025465521664 n^{6} - 1497144139335936 n^{4} + 1379916145152000 n^{2} - 474054819840000\right)}\]
\[\operatorname{Wg}([5, 2, 1, 1, 1, 1]) = \frac{- 14 n^{8} + 1902 n^{6} - 57796 n^{4} + 304788 n^{2} + 1139760}{n^{2} \left(n^{22} - 326 n^{20} + 42511 n^{18} - 2882036 n^{16} + 111145711 n^{14} - 2514183686 n^{12} + 33325295041 n^{10} - 253187957216 n^{8} + 1061276784736 n^{6} - 2307378836736 n^{4} + 2291382432000 n^{2} - 823011840000\right)}\]
\[\operatorname{Wg}([4, 3, 1, 1, 1, 1]) = \frac{- 10 n^{10} + 1702 n^{8} - 71504 n^{6} - 521212 n^{4} + 50868624 n^{2} - 167034240}{n^{2} \left(n^{24} - 390 n^{22} + 63375 n^{20} - 5602740 n^{18} + 295596015 n^{16} - 9627509190 n^{14} + 194233050945 n^{12} - 2386006839840 n^{10} + 17265306046560 n^{8} - 70229093059840 n^{6} + 149963627983104 n^{4} - 147471487488000 n^{2} + 52672757760000\right)}\]
\[\operatorname{Wg}([7, 1, 1, 1, 1]) = \frac{132 n^{12} - 27852 n^{10} + 1995708 n^{8} - 57849924 n^{6} + 649273680 n^{4} - 2424242304 n^{2} + 1437004800}{n^{3} \left(n^{26} - 399 n^{24} + 66885 n^{22} - 6173115 n^{20} + 346020675 n^{18} - 12287873325 n^{16} + 280880633655 n^{14} - 4134104298345 n^{12} + 38739367605120 n^{10} - 225616847478880 n^{8} + 782025465521664 n^{6} - 1497144139335936 n^{4} + 1379916145152000 n^{2} - 474054819840000\right)}\]
\[\operatorname{Wg}([2, 2, 2, 2, 1, 1, 1]) = \frac{n^{14} - 236 n^{12} + 21033 n^{10} - 889090 n^{8} + 16846604 n^{6} - 75657384 n^{4} - 608866848 n^{2} + 2482099200}{n^{3} \left(n^{26} - 399 n^{24} + 66885 n^{22} - 6173115 n^{20} + 346020675 n^{18} - 12287873325 n^{16} + 280880633655 n^{14} - 4134104298345 n^{12} + 38739367605120 n^{10} - 225616847478880 n^{8} + 782025465521664 n^{6} - 1497144139335936 n^{4} + 1379916145152000 n^{2} - 474054819840000\right)}\]
\[\operatorname{Wg}([4, 2, 2, 1, 1, 1]) = \frac{- 5 n^{10} + 917 n^{8} - 58276 n^{6} + 1799668 n^{4} - 31856304 n^{2} + 168658560}{n^{2} \left(n^{24} - 390 n^{22} + 63375 n^{20} - 5602740 n^{18} + 295596015 n^{16} - 9627509190 n^{14} + 194233050945 n^{12} - 2386006839840 n^{10} + 17265306046560 n^{8} - 70229093059840 n^{6} + 149963627983104 n^{4} - 147471487488000 n^{2} + 52672757760000\right)}\]
\[\operatorname{Wg}([3, 3, 2, 1, 1, 1]) = \frac{- 4 n^{10} + 708 n^{8} - 45506 n^{6} + 1745352 n^{4} - 47293830 n^{2} + 468711360}{n^{2} \left(n^{24} - 395 n^{22} + 65305 n^{20} - 5911895 n^{18} + 322373095 n^{16} - 10998380945 n^{14} + 236887109875 n^{12} - 3186555858845 n^{10} + 25993144169740 n^{8} - 121644270799920 n^{6} + 295448382321984 n^{4} - 315350610048000 n^{2} + 118513704960000\right)}\]
\[\operatorname{Wg}([6, 2, 1, 1, 1]) = \frac{42 n^{12} - 7242 n^{10} + 387858 n^{8} - 7443534 n^{6} + 53462700 n^{4} - 43980624 n^{2} + 130636800}{n^{3} \left(n^{26} - 399 n^{24} + 66885 n^{22} - 6173115 n^{20} + 346020675 n^{18} - 12287873325 n^{16} + 280880633655 n^{14} - 4134104298345 n^{12} + 38739367605120 n^{10} - 225616847478880 n^{8} + 782025465521664 n^{6} - 1497144139335936 n^{4} + 1379916145152000 n^{2} - 474054819840000\right)}\]
\[\operatorname{Wg}([5, 3, 1, 1, 1]) = \frac{28 n^{12} - 3493 n^{10} + 27356 n^{8} + 7454503 n^{6} - 191481234 n^{4} + 1085759640 n^{2} - 1241049600}{n^{3} \left(n^{26} - 399 n^{24} + 66885 n^{22} - 6173115 n^{20} + 346020675 n^{18} - 12287873325 n^{16} + 280880633655 n^{14} - 4134104298345 n^{12} + 38739367605120 n^{10} - 225616847478880 n^{8} + 782025465521664 n^{6} - 1497144139335936 n^{4} + 1379916145152000 n^{2} - 474054819840000\right)}\]
\[\operatorname{Wg}([4, 4, 1, 1, 1]) = \frac{25 n^{12} - 2620 n^{10} - 66379 n^{8} + 11938846 n^{6} - 279926736 n^{4} + 1516001184 n^{2} - 653184000}{n^{3} \left(n^{26} - 399 n^{24} + 66885 n^{22} - 6173115 n^{20} + 346020675 n^{18} - 12287873325 n^{16} + 280880633655 n^{14} - 4134104298345 n^{12} + 38739367605120 n^{10} - 225616847478880 n^{8} + 782025465521664 n^{6} - 1497144139335936 n^{4} + 1379916145152000 n^{2} - 474054819840000\right)}\]
\[\operatorname{Wg}([8, 1, 1, 1]) = \frac{- 429 n^{8} + 71643 n^{6} - 3540966 n^{4} + 51552072 n^{2} - 84839040}{n^{2} \left(n^{24} - 390 n^{22} + 63375 n^{20} - 5602740 n^{18} + 295596015 n^{16} - 9627509190 n^{14} + 194233050945 n^{12} - 2386006839840 n^{10} + 17265306046560 n^{8} - 70229093059840 n^{6} + 149963627983104 n^{4} - 147471487488000 n^{2} + 52672757760000\right)}\]
\[\operatorname{Wg}([3, 2, 2, 2, 1, 1]) = \frac{- 2 n^{8} + 198 n^{6} - 9012 n^{4} + 58928 n^{2} + 2211840}{n^{2} \left(n^{22} - 309 n^{20} + 38346 n^{18} - 2496714 n^{16} + 93362181 n^{14} - 2065172529 n^{12} + 26954076096 n^{10} - 202726676064 n^{8} + 844445285376 n^{6} - 1829024944384 n^{4} + 1812607488000 n^{2} - 650280960000\right)}\]
\[\operatorname{Wg}([5, 2, 2, 1, 1]) = \frac{14 n^{10} - 934 n^{8} + 36400 n^{6} - 654472 n^{4} - 125920 n^{2} + 11289600}{n^{3} \left(n^{24} - 318 n^{22} + 41127 n^{20} - 2841828 n^{18} + 115832607 n^{16} - 2905432158 n^{14} + 45540628857 n^{12} - 445313360928 n^{10} + 2668985369952 n^{8} - 9429032512768 n^{6} + 18273831987456 n^{4} - 16963748352000 n^{2} + 5852528640000\right)}\]
\[\operatorname{Wg}([4, 3, 2, 1, 1]) = \frac{10 n^{8} - 306 n^{6} + 24168 n^{4} - 966016 n^{2} + 1075200}{n^{3} \left(n^{22} - 309 n^{20} + 38346 n^{18} - 2496714 n^{16} + 93362181 n^{14} - 2065172529 n^{12} + 26954076096 n^{10} - 202726676064 n^{8} + 844445285376 n^{6} - 1829024944384 n^{4} + 1812607488000 n^{2} - 650280960000\right)}\]
\[\operatorname{Wg}([7, 2, 1, 1]) = \frac{- 132 n^{6} + 6094 n^{4} - 105754 n^{2} + 1995840}{n^{2} \left(n^{22} - 314 n^{20} + 39871 n^{18} - 2682344 n^{16} + 105103231 n^{14} - 2485019234 n^{12} + 35600551921 n^{10} - 302911153244 n^{8} + 1457340756976 n^{6} - 3599669484864 n^{4} + 3875154048000 n^{2} - 1463132160000\right)}\]
\[\operatorname{Wg}([3, 3, 3, 1, 1]) = \frac{8 n^{8} - 184 n^{6} + 40028 n^{4} - 1793520 n^{2} + 3225600}{n^{3} \left(n^{22} - 309 n^{20} + 38346 n^{18} - 2496714 n^{16} + 93362181 n^{14} - 2065172529 n^{12} + 26954076096 n^{10} - 202726676064 n^{8} + 844445285376 n^{6} - 1829024944384 n^{4} + 1812607488000 n^{2} - 650280960000\right)}\]
\[\operatorname{Wg}([6, 3, 1, 1]) = \frac{- 84 n^{6} - 2076 n^{4} + 208848 n^{2} - 140160}{n^{2} \left(n^{22} - 309 n^{20} + 38346 n^{18} - 2496714 n^{16} + 93362181 n^{14} - 2065172529 n^{12} + 26954076096 n^{10} - 202726676064 n^{8} + 844445285376 n^{6} - 1829024944384 n^{4} + 1812607488000 n^{2} - 650280960000\right)}\]
\[\operatorname{Wg}([5, 4, 1, 1]) = \frac{- 70 n^{8} - 4158 n^{6} + 408324 n^{4} - 5866448 n^{2} + 16007040}{n^{2} \left(n^{24} - 318 n^{22} + 41127 n^{20} - 2841828 n^{18} + 115832607 n^{16} - 2905432158 n^{14} + 45540628857 n^{12} - 445313360928 n^{10} + 2668985369952 n^{8} - 9429032512768 n^{6} + 18273831987456 n^{4} - 16963748352000 n^{2} + 5852528640000\right)}\]
\[\operatorname{Wg}([9, 1, 1]) = \frac{1430 n^{2} - 55484}{n \left(n^{20} - 305 n^{18} + 37126 n^{16} - 2348210 n^{14} + 83969341 n^{12} - 1729295165 n^{10} + 20036895436 n^{8} - 122579094320 n^{6} + 354128908096 n^{4} - 412509312000 n^{2} + 162570240000\right)}\]
\[\operatorname{Wg}([2, 2, 2, 2, 2, 1]) = \frac{- n^{12} + 194 n^{10} - 15285 n^{8} + 501520 n^{6} - 6974924 n^{4} + 94322736 n^{2} + 2034408960}{n^{2} \left(n^{26} - 399 n^{24} + 66885 n^{22} - 6173115 n^{20} + 346020675 n^{18} - 12287873325 n^{16} + 280880633655 n^{14} - 4134104298345 n^{12} + 38739367605120 n^{10} - 225616847478880 n^{8} + 782025465521664 n^{6} - 1497144139335936 n^{4} + 1379916145152000 n^{2} - 474054819840000\right)}\]
\[\operatorname{Wg}([4, 2, 2, 2, 1]) = \frac{5 n^{12} - 684 n^{10} + 45753 n^{8} - 1207274 n^{6} - 4948008 n^{4} - 261816192 n^{2} + 261273600}{n^{3} \left(n^{26} - 399 n^{24} + 66885 n^{22} - 6173115 n^{20} + 346020675 n^{18} - 12287873325 n^{16} + 280880633655 n^{14} - 4134104298345 n^{12} + 38739367605120 n^{10} - 225616847478880 n^{8} + 782025465521664 n^{6} - 1497144139335936 n^{4} + 1379916145152000 n^{2} - 474054819840000\right)}\]
\[\operatorname{Wg}([3, 3, 2, 2, 1]) = \frac{4 n^{12} - 508 n^{10} + 37412 n^{8} - 983924 n^{6} - 24491736 n^{4} + 203975712 n^{2} - 130636800}{n^{3} \left(n^{26} - 399 n^{24} + 66885 n^{22} - 6173115 n^{20} + 346020675 n^{18} - 12287873325 n^{16} + 280880633655 n^{14} - 4134104298345 n^{12} + 38739367605120 n^{10} - 225616847478880 n^{8} + 782025465521664 n^{6} - 1497144139335936 n^{4} + 1379916145152000 n^{2} - 474054819840000\right)}\]
\[\operatorname{Wg}([6, 2, 2, 1]) = \frac{- 42 n^{10} + 4164 n^{8} - 204042 n^{6} + 5352816 n^{4} + 97818624 n^{2} - 930579840}{n^{2} \left(n^{26} - 399 n^{24} + 66885 n^{22} - 6173115 n^{20} + 346020675 n^{18} - 12287873325 n^{16} + 280880633655 n^{14} - 4134104298345 n^{12} + 38739367605120 n^{10} - 225616847478880 n^{8} + 782025465521664 n^{6} - 1497144139335936 n^{4} + 1379916145152000 n^{2} - 474054819840000\right)}\]
\[\operatorname{Wg}([5, 3, 2, 1]) = \frac{- 28 n^{6} - 515 n^{4} - 108597 n^{2} - 331740}{n^{2} \left(n^{22} - 326 n^{20} + 42511 n^{18} - 2882036 n^{16} + 111145711 n^{14} - 2514183686 n^{12} + 33325295041 n^{10} - 253187957216 n^{8} + 1061276784736 n^{6} - 2307378836736 n^{4} + 2291382432000 n^{2} - 823011840000\right)}\]
\[\operatorname{Wg}([4, 4, 2, 1]) = \frac{- 25 n^{8} - 710 n^{6} - 99585 n^{4} + 1884240 n^{2} - 17645040}{n^{2} \left(n^{24} - 335 n^{22} + 45445 n^{20} - 3264635 n^{18} + 137084035 n^{16} - 3514495085 n^{14} + 55952948215 n^{12} - 553115612585 n^{10} + 3339968399680 n^{8} - 11858869899360 n^{6} + 23057791962624 n^{4} - 21445453728000 n^{2} + 7407106560000\right)}\]
\[\operatorname{Wg}([8, 2, 1]) = \frac{429 n^{4} - 4433 n^{2} + 587444}{n \left(n^{22} - 326 n^{20} + 42511 n^{18} - 2882036 n^{16} + 111145711 n^{14} - 2514183686 n^{12} + 33325295041 n^{10} - 253187957216 n^{8} + 1061276784736 n^{6} - 2307378836736 n^{4} + 2291382432000 n^{2} - 823011840000\right)}\]
\[\operatorname{Wg}([4, 3, 3, 1]) = \frac{- 20 n^{10} + 676 n^{8} - 165644 n^{6} + 18713484 n^{4} - 353590416 n^{2} + 1005644160}{n^{2} \left(n^{26} - 399 n^{24} + 66885 n^{22} - 6173115 n^{20} + 346020675 n^{18} - 12287873325 n^{16} + 280880633655 n^{14} - 4134104298345 n^{12} + 38739367605120 n^{10} - 225616847478880 n^{8} + 782025465521664 n^{6} - 1497144139335936 n^{4} + 1379916145152000 n^{2} - 474054819840000\right)}\]
\[\operatorname{Wg}([7, 3, 1]) = \frac{264 n^{10} + 66 n^{8} - 1259412 n^{6} + 3390354 n^{4} + 322525368 n^{2} - 718502400}{n^{3} \left(n^{26} - 399 n^{24} + 66885 n^{22} - 6173115 n^{20} + 346020675 n^{18} - 12287873325 n^{16} + 280880633655 n^{14} - 4134104298345 n^{12} + 38739367605120 n^{10} - 225616847478880 n^{8} + 782025465521664 n^{6} - 1497144139335936 n^{4} + 1379916145152000 n^{2} - 474054819840000\right)}\]
\[\operatorname{Wg}([6, 4, 1]) = \frac{210 n^{10} + 14628 n^{8} - 2649822 n^{6} + 57880872 n^{4} - 390305088 n^{2} - 130636800}{n^{3} \left(n^{26} - 399 n^{24} + 66885 n^{22} - 6173115 n^{20} + 346020675 n^{18} - 12287873325 n^{16} + 280880633655 n^{14} - 4134104298345 n^{12} + 38739367605120 n^{10} - 225616847478880 n^{8} + 782025465521664 n^{6} - 1497144139335936 n^{4} + 1379916145152000 n^{2} - 474054819840000\right)}\]
\[\operatorname{Wg}([5, 5, 1]) = \frac{196 n^{10} + 18816 n^{8} - 3114636 n^{6} + 80923304 n^{4} - 852697440 n^{2} + 1698278400}{n^{3} \left(n^{26} - 399 n^{24} + 66885 n^{22} - 6173115 n^{20} + 346020675 n^{18} - 12287873325 n^{16} + 280880633655 n^{14} - 4134104298345 n^{12} + 38739367605120 n^{10} - 225616847478880 n^{8} + 782025465521664 n^{6} - 1497144139335936 n^{4} + 1379916145152000 n^{2} - 474054819840000\right)}\]
\[\operatorname{Wg}([10, 1]) = \frac{- 4862 n^{2} + 318240}{n^{2} \left(n^{20} - 385 n^{18} + 61446 n^{16} - 5293970 n^{14} + 268880381 n^{12} - 8261931405 n^{10} + 151847872396 n^{8} - 1593719752240 n^{6} + 8689315795776 n^{4} - 20407635072000 n^{2} + 13168189440000\right)}\]
\[\operatorname{Wg}([3, 2, 2, 2, 2]) = \frac{2 n^{12} - 276 n^{10} + 21546 n^{8} - 213488 n^{6} + 20918712 n^{4} + 668987424 n^{2} - 4572288000}{n^{3} \left(n^{26} - 399 n^{24} + 66885 n^{22} - 6173115 n^{20} + 346020675 n^{18} - 12287873325 n^{16} + 280880633655 n^{14} - 4134104298345 n^{12} + 38739367605120 n^{10} - 225616847478880 n^{8} + 782025465521664 n^{6} - 1497144139335936 n^{4} + 1379916145152000 n^{2} - 474054819840000\right)}\]
\[\operatorname{Wg}([5, 2, 2, 2]) = \frac{- 14 n^{10} + 1128 n^{8} - 98694 n^{6} - 871108 n^{4} - 107204112 n^{2} + 62933760}{n^{2} \left(n^{26} - 399 n^{24} + 66885 n^{22} - 6173115 n^{20} + 346020675 n^{18} - 12287873325 n^{16} + 280880633655 n^{14} - 4134104298345 n^{12} + 38739367605120 n^{10} - 225616847478880 n^{8} + 782025465521664 n^{6} - 1497144139335936 n^{4} + 1379916145152000 n^{2} - 474054819840000\right)}\]
\[\operatorname{Wg}([4, 3, 2, 2]) = \frac{- 10 n^{8} + 470 n^{6} - 79900 n^{4} - 2159760 n^{2} - 51315840}{n^{2} \left(n^{24} - 390 n^{22} + 63375 n^{20} - 5602740 n^{18} + 295596015 n^{16} - 9627509190 n^{14} + 194233050945 n^{12} - 2386006839840 n^{10} + 17265306046560 n^{8} - 70229093059840 n^{6} + 149963627983104 n^{4} - 147471487488000 n^{2} + 52672757760000\right)}\]
\[\operatorname{Wg}([7, 2, 2]) = \frac{132 n^{10} - 5984 n^{8} + 618772 n^{6} + 12543784 n^{4} - 146212704 n^{2} + 1437004800}{n^{3} \left(n^{26} - 399 n^{24} + 66885 n^{22} - 6173115 n^{20} + 346020675 n^{18} - 12287873325 n^{16} + 280880633655 n^{14} - 4134104298345 n^{12} + 38739367605120 n^{10} - 225616847478880 n^{8} + 782025465521664 n^{6} - 1497144139335936 n^{4} + 1379916145152000 n^{2} - 474054819840000\right)}\]
\[\operatorname{Wg}([3, 3, 3, 2]) = \frac{- 8 n^{10} + 400 n^{8} - 89384 n^{6} - 2455200 n^{4} + 75327552 n^{2} + 1140687360}{n^{2} \left(n^{26} - 399 n^{24} + 66885 n^{22} - 6173115 n^{20} + 346020675 n^{18} - 12287873325 n^{16} + 280880633655 n^{14} - 4134104298345 n^{12} + 38739367605120 n^{10} - 225616847478880 n^{8} + 782025465521664 n^{6} - 1497144139335936 n^{4} + 1379916145152000 n^{2} - 474054819840000\right)}\]
\[\operatorname{Wg}([6, 3, 2]) = \frac{84 n^{10} + 1428 n^{8} + 441420 n^{6} + 5577852 n^{4} - 275035824 n^{2} + 130636800}{n^{3} \left(n^{26} - 399 n^{24} + 66885 n^{22} - 6173115 n^{20} + 346020675 n^{18} - 12287873325 n^{16} + 280880633655 n^{14} - 4134104298345 n^{12} + 38739367605120 n^{10} - 225616847478880 n^{8} + 782025465521664 n^{6} - 1497144139335936 n^{4} + 1379916145152000 n^{2} - 474054819840000\right)}\]
\[\operatorname{Wg}([5, 4, 2]) = \frac{70 n^{8} + 4770 n^{6} + 387960 n^{4} + 1391360 n^{2} + 174182400}{n^{3} \left(n^{24} - 390 n^{22} + 63375 n^{20} - 5602740 n^{18} + 295596015 n^{16} - 9627509190 n^{14} + 194233050945 n^{12} - 2386006839840 n^{10} + 17265306046560 n^{8} - 70229093059840 n^{6} + 149963627983104 n^{4} - 147471487488000 n^{2} + 52672757760000\right)}\]
\[\operatorname{Wg}([9, 2]) = \frac{- 1430 n^{4} + 20150 n^{2} - 4343040}{n^{2} \left(n^{22} - 386 n^{20} + 61831 n^{18} - 5355416 n^{16} + 274174351 n^{14} - 8530811786 n^{12} + 160109803801 n^{10} - 1745567624636 n^{8} + 10283035548016 n^{6} - 29096950867776 n^{4} + 33575824512000 n^{2} - 13168189440000\right)}\]
\[\operatorname{Wg}([5, 3, 3]) = \frac{56 n^{10} + 2996 n^{8} + 887264 n^{6} - 29905596 n^{4} + 50788080 n^{2} - 261273600}{n^{3} \left(n^{26} - 399 n^{24} + 66885 n^{22} - 6173115 n^{20} + 346020675 n^{18} - 12287873325 n^{16} + 280880633655 n^{14} - 4134104298345 n^{12} + 38739367605120 n^{10} - 225616847478880 n^{8} + 782025465521664 n^{6} - 1497144139335936 n^{4} + 1379916145152000 n^{2} - 474054819840000\right)}\]
\[\operatorname{Wg}([4, 4, 3]) = \frac{50 n^{10} + 3500 n^{8} + 1002050 n^{6} - 44883840 n^{4} + 477156960 n^{2} + 1698278400}{n^{3} \left(n^{26} - 399 n^{24} + 66885 n^{22} - 6173115 n^{20} + 346020675 n^{18} - 12287873325 n^{16} + 280880633655 n^{14} - 4134104298345 n^{12} + 38739367605120 n^{10} - 225616847478880 n^{8} + 782025465521664 n^{6} - 1497144139335936 n^{4} + 1379916145152000 n^{2} - 474054819840000\right)}\]
\[\operatorname{Wg}([8, 3]) = \frac{- 858 n^{6} - 70590 n^{4} - 1070472 n^{2} + 74655360}{n^{2} \left(n^{24} - 390 n^{22} + 63375 n^{20} - 5602740 n^{18} + 295596015 n^{16} - 9627509190 n^{14} + 194233050945 n^{12} - 2386006839840 n^{10} + 17265306046560 n^{8} - 70229093059840 n^{6} + 149963627983104 n^{4} - 147471487488000 n^{2} + 52672757760000\right)}\]
\[\operatorname{Wg}([7, 4]) = \frac{- 660 n^{8} - 111720 n^{6} + 3546060 n^{4} - 25085520 n^{2} - 494605440}{n^{2} \left(n^{26} - 399 n^{24} + 66885 n^{22} - 6173115 n^{20} + 346020675 n^{18} - 12287873325 n^{16} + 280880633655 n^{14} - 4134104298345 n^{12} + 38739367605120 n^{10} - 225616847478880 n^{8} + 782025465521664 n^{6} - 1497144139335936 n^{4} + 1379916145152000 n^{2} - 474054819840000\right)}\]
\[\operatorname{Wg}([6, 5]) = \frac{- 588 n^{8} - 132888 n^{6} + 5827668 n^{4} - 131855472 n^{2} + 1334309760}{n^{2} \left(n^{26} - 399 n^{24} + 66885 n^{22} - 6173115 n^{20} + 346020675 n^{18} - 12287873325 n^{16} + 280880633655 n^{14} - 4134104298345 n^{12} + 38739367605120 n^{10} - 225616847478880 n^{8} + 782025465521664 n^{6} - 1497144139335936 n^{4} + 1379916145152000 n^{2} - 474054819840000\right)}\]
\[\operatorname{Wg}([11]) = \frac{16796}{n \left(n^{20} - 385 n^{18} + 61446 n^{16} - 5293970 n^{14} + 268880381 n^{12} - 8261931405 n^{10} + 151847872396 n^{8} - 1593719752240 n^{6} + 8689315795776 n^{4} - 20407635072000 n^{2} + 13168189440000\right)}\]