Weingarten functions for p = 10
Below are the values of the Weingarten function for permutation size p = 10. The input is given as a partition of p. You can also download them as a text file or as a python pickle file.
\[\operatorname{Wg}([1, 1, 1, 1, 1, 1, 1, 1, 1, 1]) = \frac{n^{16} - 254 n^{14} + 25165 n^{12} - 1239500 n^{10} + 32153848 n^{8} - 432276152 n^{6} + 2813672556 n^{4} - 7651234224 n^{2} + 5272646400}{n^{2} \left(n^{24} - 299 n^{22} + 36985 n^{20} - 2474615 n^{18} + 98559175 n^{16} - 2431955825 n^{14} + 37685051155 n^{12} - 365599182845 n^{10} + 2179449320620 n^{8} - 7671915416880 n^{6} + 14833923833664 n^{4} - 13751755969536 n^{2} + 4740548198400\right)}\]
\[\operatorname{Wg}([2, 1, 1, 1, 1, 1, 1, 1, 1]) = \frac{- n^{16} + 238 n^{14} - 21637 n^{12} + 950092 n^{10} - 21109312 n^{8} + 229937848 n^{6} - 1117994460 n^{4} + 1912326192 n^{2} - 640120320}{n^{3} \left(n^{24} - 299 n^{22} + 36985 n^{20} - 2474615 n^{18} + 98559175 n^{16} - 2431955825 n^{14} + 37685051155 n^{12} - 365599182845 n^{10} + 2179449320620 n^{8} - 7671915416880 n^{6} + 14833923833664 n^{4} - 13751755969536 n^{2} + 4740548198400\right)}\]
\[\operatorname{Wg}([3, 1, 1, 1, 1, 1, 1, 1]) = \frac{2 n^{12} - 423 n^{10} + 32369 n^{8} - 1089246 n^{6} + 15489074 n^{4} - 72558096 n^{2} + 64340640}{n^{2} \left(n^{22} - 290 n^{20} + 34375 n^{18} - 2165240 n^{16} + 79072015 n^{14} - 1720307690 n^{12} + 22202281945 n^{10} - 165778645340 n^{8} + 687441512560 n^{6} - 1484941803840 n^{4} + 1469447599104 n^{2} - 526727577600\right)}\]
\[\operatorname{Wg}([2, 2, 1, 1, 1, 1, 1, 1]) = \frac{n^{14} - 216 n^{12} + 17335 n^{10} - 648702 n^{8} + 11758858 n^{6} - 98555292 n^{4} + 324025776 n^{2} - 282683520}{n^{2} \left(n^{24} - 299 n^{22} + 36985 n^{20} - 2474615 n^{18} + 98559175 n^{16} - 2431955825 n^{14} + 37685051155 n^{12} - 365599182845 n^{10} + 2179449320620 n^{8} - 7671915416880 n^{6} + 14833923833664 n^{4} - 13751755969536 n^{2} + 4740548198400\right)}\]
\[\operatorname{Wg}([4, 1, 1, 1, 1, 1, 1]) = \frac{- 5 n^{14} + 1014 n^{12} - 74231 n^{10} + 2418048 n^{8} - 35416562 n^{6} + 216946488 n^{4} - 463655232 n^{2} + 182891520}{n^{3} \left(n^{24} - 299 n^{22} + 36985 n^{20} - 2474615 n^{18} + 98559175 n^{16} - 2431955825 n^{14} + 37685051155 n^{12} - 365599182845 n^{10} + 2179449320620 n^{8} - 7671915416880 n^{6} + 14833923833664 n^{4} - 13751755969536 n^{2} + 4740548198400\right)}\]
\[\operatorname{Wg}([3, 2, 1, 1, 1, 1, 1]) = \frac{- 2 n^{14} + 379 n^{12} - 25488 n^{10} + 752393 n^{8} - 10091572 n^{6} + 60012618 n^{4} - 117055368 n^{2} + 45722880}{n^{3} \left(n^{24} - 299 n^{22} + 36985 n^{20} - 2474615 n^{18} + 98559175 n^{16} - 2431955825 n^{14} + 37685051155 n^{12} - 365599182845 n^{10} + 2179449320620 n^{8} - 7671915416880 n^{6} + 14833923833664 n^{4} - 13751755969536 n^{2} + 4740548198400\right)}\]
\[\operatorname{Wg}([5, 1, 1, 1, 1, 1]) = \frac{14 n^{12} - 2576 n^{10} + 165298 n^{8} - 4487812 n^{6} + 50921388 n^{4} - 215849592 n^{2} + 209653920}{n^{2} \left(n^{24} - 299 n^{22} + 36985 n^{20} - 2474615 n^{18} + 98559175 n^{16} - 2431955825 n^{14} + 37685051155 n^{12} - 365599182845 n^{10} + 2179449320620 n^{8} - 7671915416880 n^{6} + 14833923833664 n^{4} - 13751755969536 n^{2} + 4740548198400\right)}\]
\[\operatorname{Wg}([2, 2, 2, 1, 1, 1, 1]) = \frac{- n^{14} + 188 n^{12} - 12891 n^{10} + 410170 n^{8} - 6341894 n^{6} + 41526972 n^{4} - 61588944 n^{2} - 91445760}{n^{3} \left(n^{24} - 299 n^{22} + 36985 n^{20} - 2474615 n^{18} + 98559175 n^{16} - 2431955825 n^{14} + 37685051155 n^{12} - 365599182845 n^{10} + 2179449320620 n^{8} - 7671915416880 n^{6} + 14833923833664 n^{4} - 13751755969536 n^{2} + 4740548198400\right)}\]
\[\operatorname{Wg}([4, 2, 1, 1, 1, 1]) = \frac{5 n^{8} - 516 n^{6} + 10750 n^{4} - 39048 n^{2} + 45504}{n^{2} \left(n^{20} - 241 n^{18} + 22566 n^{16} - 1059506 n^{14} + 27156221 n^{12} - 389652861 n^{10} + 3109291756 n^{8} - 13423349296 n^{6} + 29697397056 n^{4} - 29769348096 n^{2} + 10749542400\right)}\]
\[\operatorname{Wg}([3, 3, 1, 1, 1, 1]) = \frac{4 n^{10} - 576 n^{8} + 24152 n^{6} - 250848 n^{4} - 1166796 n^{2} + 4780944}{n^{2} \left(n^{22} - 295 n^{20} + 35805 n^{18} - 2331395 n^{16} + 89233595 n^{14} - 2075021445 n^{12} + 29384965375 n^{10} - 248059321345 n^{8} + 1187212035240 n^{6} - 2923067275920 n^{4} + 3141654729984 n^{2} - 1185137049600\right)}\]
\[\operatorname{Wg}([6, 1, 1, 1, 1]) = \frac{- 42 n^{12} + 6828 n^{10} - 370614 n^{8} + 8018976 n^{6} - 67613724 n^{4} + 190353456 n^{2} - 91445760}{n^{3} \left(n^{24} - 299 n^{22} + 36985 n^{20} - 2474615 n^{18} + 98559175 n^{16} - 2431955825 n^{14} + 37685051155 n^{12} - 365599182845 n^{10} + 2179449320620 n^{8} - 7671915416880 n^{6} + 14833923833664 n^{4} - 13751755969536 n^{2} + 4740548198400\right)}\]
\[\operatorname{Wg}([3, 2, 2, 1, 1, 1]) = \frac{2 n^{10} - 287 n^{8} + 14167 n^{6} - 336634 n^{4} + 4176336 n^{2} - 8162784}{n^{2} \left(n^{22} - 290 n^{20} + 34375 n^{18} - 2165240 n^{16} + 79072015 n^{14} - 1720307690 n^{12} + 22202281945 n^{10} - 165778645340 n^{8} + 687441512560 n^{6} - 1484941803840 n^{4} + 1469447599104 n^{2} - 526727577600\right)}\]
\[\operatorname{Wg}([5, 2, 1, 1, 1]) = \frac{- 14 n^{12} + 1832 n^{10} - 70906 n^{8} + 859012 n^{6} - 1616340 n^{4} - 26268624 n^{2} + 45722880}{n^{3} \left(n^{24} - 299 n^{22} + 36985 n^{20} - 2474615 n^{18} + 98559175 n^{16} - 2431955825 n^{14} + 37685051155 n^{12} - 365599182845 n^{10} + 2179449320620 n^{8} - 7671915416880 n^{6} + 14833923833664 n^{4} - 13751755969536 n^{2} + 4740548198400\right)}\]
\[\operatorname{Wg}([4, 3, 1, 1, 1]) = \frac{- 10 n^{12} + 1009 n^{10} - 11372 n^{8} - 927595 n^{6} + 18341952 n^{4} - 79456464 n^{2} + 45722880}{n^{3} \left(n^{24} - 299 n^{22} + 36985 n^{20} - 2474615 n^{18} + 98559175 n^{16} - 2431955825 n^{14} + 37685051155 n^{12} - 365599182845 n^{10} + 2179449320620 n^{8} - 7671915416880 n^{6} + 14833923833664 n^{4} - 13751755969536 n^{2} + 4740548198400\right)}\]
\[\operatorname{Wg}([7, 1, 1, 1]) = \frac{132 n^{8} - 16863 n^{6} + 619311 n^{4} - 6468132 n^{2} + 9690912}{n^{2} \left(n^{22} - 290 n^{20} + 34375 n^{18} - 2165240 n^{16} + 79072015 n^{14} - 1720307690 n^{12} + 22202281945 n^{10} - 165778645340 n^{8} + 687441512560 n^{6} - 1484941803840 n^{4} + 1469447599104 n^{2} - 526727577600\right)}\]
\[\operatorname{Wg}([2, 2, 2, 2, 1, 1]) = \frac{n^{10} - 90 n^{8} + 3285 n^{6} - 31240 n^{4} - 182916 n^{2} + 3039120}{n^{2} \left(n^{22} - 235 n^{20} + 21945 n^{18} - 1070135 n^{16} + 30070535 n^{14} - 507441585 n^{12} + 5208789715 n^{10} - 32236641085 n^{8} + 116304291180 n^{6} - 228440781360 n^{4} + 213713826624 n^{2} - 74071065600\right)}\]
\[\operatorname{Wg}([4, 2, 2, 1, 1]) = \frac{- 5 n^{6} + 203 n^{4} - 6494 n^{2} + 89576}{n \left(n^{20} - 226 n^{18} + 19911 n^{16} - 890936 n^{14} + 22052111 n^{12} - 308972586 n^{10} + 2428036441 n^{8} - 10384313116 n^{6} + 22845473136 n^{4} - 22831523136 n^{2} + 8230118400\right)}\]
\[\operatorname{Wg}([3, 3, 2, 1, 1]) = \frac{- 4 n^{10} + 152 n^{8} - 7870 n^{6} + 217548 n^{4} - 1442826 n^{2} + 1428840}{n^{3} \left(n^{22} - 235 n^{20} + 21945 n^{18} - 1070135 n^{16} + 30070535 n^{14} - 507441585 n^{12} + 5208789715 n^{10} - 32236641085 n^{8} + 116304291180 n^{6} - 228440781360 n^{4} + 213713826624 n^{2} - 74071065600\right)}\]
\[\operatorname{Wg}([6, 2, 1, 1]) = \frac{42 n^{6} - 1230 n^{4} + 8046 n^{2} - 75978}{n^{2} \left(n^{20} - 231 n^{18} + 21021 n^{16} - 986051 n^{14} + 26126331 n^{12} - 402936261 n^{10} + 3597044671 n^{8} - 17848462401 n^{6} + 44910441576 n^{4} - 48799015056 n^{2} + 18517766400\right)}\]
\[\operatorname{Wg}([5, 3, 1, 1]) = \frac{28 n^{6} + 665 n^{4} - 43113 n^{2} + 104580}{n^{2} \left(n^{20} - 226 n^{18} + 19911 n^{16} - 890936 n^{14} + 22052111 n^{12} - 308972586 n^{10} + 2428036441 n^{8} - 10384313116 n^{6} + 22845473136 n^{4} - 22831523136 n^{2} + 8230118400\right)}\]
\[\operatorname{Wg}([4, 4, 1, 1]) = \frac{25 n^{8} + 870 n^{6} - 69823 n^{4} + 772560 n^{2} - 1369872}{n^{2} \left(n^{22} - 235 n^{20} + 21945 n^{18} - 1070135 n^{16} + 30070535 n^{14} - 507441585 n^{12} + 5208789715 n^{10} - 32236641085 n^{8} + 116304291180 n^{6} - 228440781360 n^{4} + 213713826624 n^{2} - 74071065600\right)}\]
\[\operatorname{Wg}([8, 1, 1]) = \frac{- 429 n^{2} + 11869}{n \left(n^{18} - 222 n^{16} + 19023 n^{14} - 814844 n^{12} + 18792735 n^{10} - 233801646 n^{8} + 1492829857 n^{6} - 4412993688 n^{4} + 5193498384 n^{2} - 2057529600\right)}\]
\[\operatorname{Wg}([3, 2, 2, 2, 1]) = \frac{- 2 n^{12} + 219 n^{10} - 11766 n^{8} + 221027 n^{6} + 2702418 n^{4} - 26741016 n^{2} + 45722880}{n^{3} \left(n^{24} - 299 n^{22} + 36985 n^{20} - 2474615 n^{18} + 98559175 n^{16} - 2431955825 n^{14} + 37685051155 n^{12} - 365599182845 n^{10} + 2179449320620 n^{8} - 7671915416880 n^{6} + 14833923833664 n^{4} - 13751755969536 n^{2} + 4740548198400\right)}\]
\[\operatorname{Wg}([5, 2, 2, 1]) = \frac{14 n^{10} - 1004 n^{8} + 39718 n^{6} - 1098496 n^{4} - 1873512 n^{2} + 62687520}{n^{2} \left(n^{24} - 299 n^{22} + 36985 n^{20} - 2474615 n^{18} + 98559175 n^{16} - 2431955825 n^{14} + 37685051155 n^{12} - 365599182845 n^{10} + 2179449320620 n^{8} - 7671915416880 n^{6} + 14833923833664 n^{4} - 13751755969536 n^{2} + 4740548198400\right)}\]
\[\operatorname{Wg}([4, 3, 2, 1]) = \frac{10 n^{6} + 137 n^{4} + 28932 n^{2} - 133344}{n^{2} \left(n^{20} - 241 n^{18} + 22566 n^{16} - 1059506 n^{14} + 27156221 n^{12} - 389652861 n^{10} + 3109291756 n^{8} - 13423349296 n^{6} + 29697397056 n^{4} - 29769348096 n^{2} + 10749542400\right)}\]
\[\operatorname{Wg}([7, 2, 1]) = \frac{- 132 n^{4} + 121 n^{2} - 79684}{n \left(n^{20} - 241 n^{18} + 22566 n^{16} - 1059506 n^{14} + 27156221 n^{12} - 389652861 n^{10} + 3109291756 n^{8} - 13423349296 n^{6} + 29697397056 n^{4} - 29769348096 n^{2} + 10749542400\right)}\]
\[\operatorname{Wg}([3, 3, 3, 1]) = \frac{8 n^{10} - 292 n^{8} + 39704 n^{6} - 3139956 n^{4} + 45793368 n^{2} - 125429472}{n^{2} \left(n^{24} - 299 n^{22} + 36985 n^{20} - 2474615 n^{18} + 98559175 n^{16} - 2431955825 n^{14} + 37685051155 n^{12} - 365599182845 n^{10} + 2179449320620 n^{8} - 7671915416880 n^{6} + 14833923833664 n^{4} - 13751755969536 n^{2} + 4740548198400\right)}\]
\[\operatorname{Wg}([6, 3, 1]) = \frac{- 84 n^{10} - 618 n^{8} + 318360 n^{6} - 3678402 n^{4} - 3413016 n^{2} + 45722880}{n^{3} \left(n^{24} - 299 n^{22} + 36985 n^{20} - 2474615 n^{18} + 98559175 n^{16} - 2431955825 n^{14} + 37685051155 n^{12} - 365599182845 n^{10} + 2179449320620 n^{8} - 7671915416880 n^{6} + 14833923833664 n^{4} - 13751755969536 n^{2} + 4740548198400\right)}\]
\[\operatorname{Wg}([5, 4, 1]) = \frac{- 70 n^{10} - 3584 n^{8} + 539266 n^{6} - 10376716 n^{4} + 64515024 n^{2} - 45722880}{n^{3} \left(n^{24} - 299 n^{22} + 36985 n^{20} - 2474615 n^{18} + 98559175 n^{16} - 2431955825 n^{14} + 37685051155 n^{12} - 365599182845 n^{10} + 2179449320620 n^{8} - 7671915416880 n^{6} + 14833923833664 n^{4} - 13751755969536 n^{2} + 4740548198400\right)}\]
\[\operatorname{Wg}([9, 1]) = \frac{1430 n^{2} - 72072}{n^{2} \left(n^{18} - 285 n^{16} + 32946 n^{14} - 1999370 n^{12} + 68943381 n^{10} - 1367593305 n^{8} + 15088541896 n^{6} - 84865562640 n^{4} + 202759531776 n^{2} - 131681894400\right)}\]
\[\operatorname{Wg}([2, 2, 2, 2, 2]) = \frac{- n^{12} + 114 n^{10} - 6645 n^{8} + 52480 n^{6} - 3861804 n^{4} - 82670544 n^{2} + 457228800}{n^{3} \left(n^{24} - 299 n^{22} + 36985 n^{20} - 2474615 n^{18} + 98559175 n^{16} - 2431955825 n^{14} + 37685051155 n^{12} - 365599182845 n^{10} + 2179449320620 n^{8} - 7671915416880 n^{6} + 14833923833664 n^{4} - 13751755969536 n^{2} + 4740548198400\right)}\]
\[\operatorname{Wg}([4, 2, 2, 2]) = \frac{5 n^{10} - 300 n^{8} + 23625 n^{6} + 255670 n^{4} + 8490600 n^{2} - 32840640}{n^{2} \left(n^{24} - 299 n^{22} + 36985 n^{20} - 2474615 n^{18} + 98559175 n^{16} - 2431955825 n^{14} + 37685051155 n^{12} - 365599182845 n^{10} + 2179449320620 n^{8} - 7671915416880 n^{6} + 14833923833664 n^{4} - 13751755969536 n^{2} + 4740548198400\right)}\]
\[\operatorname{Wg}([3, 3, 2, 2]) = \frac{4 n^{10} - 200 n^{8} + 22372 n^{6} + 390960 n^{4} - 3860496 n^{2} - 72031680}{n^{2} \left(n^{24} - 299 n^{22} + 36985 n^{20} - 2474615 n^{18} + 98559175 n^{16} - 2431955825 n^{14} + 37685051155 n^{12} - 365599182845 n^{10} + 2179449320620 n^{8} - 7671915416880 n^{6} + 14833923833664 n^{4} - 13751755969536 n^{2} + 4740548198400\right)}\]
\[\operatorname{Wg}([6, 2, 2]) = \frac{- 42 n^{10} + 1092 n^{8} - 125034 n^{6} - 1672272 n^{4} + 28165536 n^{2} - 91445760}{n^{3} \left(n^{24} - 299 n^{22} + 36985 n^{20} - 2474615 n^{18} + 98559175 n^{16} - 2431955825 n^{14} + 37685051155 n^{12} - 365599182845 n^{10} + 2179449320620 n^{8} - 7671915416880 n^{6} + 14833923833664 n^{4} - 13751755969536 n^{2} + 4740548198400\right)}\]
\[\operatorname{Wg}([5, 3, 2]) = \frac{- 28 n^{10} - 529 n^{8} - 114478 n^{6} + 868119 n^{4} + 10254276 n^{2} + 45722880}{n^{3} \left(n^{24} - 299 n^{22} + 36985 n^{20} - 2474615 n^{18} + 98559175 n^{16} - 2431955825 n^{14} + 37685051155 n^{12} - 365599182845 n^{10} + 2179449320620 n^{8} - 7671915416880 n^{6} + 14833923833664 n^{4} - 13751755969536 n^{2} + 4740548198400\right)}\]
\[\operatorname{Wg}([4, 4, 2]) = \frac{- 25 n^{10} - 950 n^{8} - 109025 n^{6} + 2119520 n^{4} - 32854320 n^{2} + 91445760}{n^{3} \left(n^{24} - 299 n^{22} + 36985 n^{20} - 2474615 n^{18} + 98559175 n^{16} - 2431955825 n^{14} + 37685051155 n^{12} - 365599182845 n^{10} + 2179449320620 n^{8} - 7671915416880 n^{6} + 14833923833664 n^{4} - 13751755969536 n^{2} + 4740548198400\right)}\]
\[\operatorname{Wg}([8, 2]) = \frac{429 n^{4} - 429 n^{2} + 720720}{n^{2} \left(n^{20} - 286 n^{18} + 33231 n^{16} - 2032316 n^{14} + 70942751 n^{12} - 1436536686 n^{10} + 16456135201 n^{8} - 99954104536 n^{6} + 287625094416 n^{4} - 334441426176 n^{2} + 131681894400\right)}\]
\[\operatorname{Wg}([4, 3, 3]) = \frac{- 20 n^{10} - 800 n^{8} - 212660 n^{6} + 7008840 n^{4} - 41631840 n^{2} - 91445760}{n^{3} \left(n^{24} - 299 n^{22} + 36985 n^{20} - 2474615 n^{18} + 98559175 n^{16} - 2431955825 n^{14} + 37685051155 n^{12} - 365599182845 n^{10} + 2179449320620 n^{8} - 7671915416880 n^{6} + 14833923833664 n^{4} - 13751755969536 n^{2} + 4740548198400\right)}\]
\[\operatorname{Wg}([7, 3]) = \frac{264 n^{6} + 20856 n^{4} + 1056 n^{2} - 7672896}{n^{2} \left(n^{22} - 290 n^{20} + 34375 n^{18} - 2165240 n^{16} + 79072015 n^{14} - 1720307690 n^{12} + 22202281945 n^{10} - 165778645340 n^{8} + 687441512560 n^{6} - 1484941803840 n^{4} + 1469447599104 n^{2} - 526727577600\right)}\]
\[\operatorname{Wg}([6, 4]) = \frac{210 n^{8} + 29316 n^{6} - 920094 n^{4} + 10458504 n^{2} - 22389696}{n^{2} \left(n^{24} - 299 n^{22} + 36985 n^{20} - 2474615 n^{18} + 98559175 n^{16} - 2431955825 n^{14} + 37685051155 n^{12} - 365599182845 n^{10} + 2179449320620 n^{8} - 7671915416880 n^{6} + 14833923833664 n^{4} - 13751755969536 n^{2} + 4740548198400\right)}\]
\[\operatorname{Wg}([5, 5]) = \frac{196 n^{8} + 32536 n^{6} - 1189916 n^{4} + 20208384 n^{2} - 150413760}{n^{2} \left(n^{24} - 299 n^{22} + 36985 n^{20} - 2474615 n^{18} + 98559175 n^{16} - 2431955825 n^{14} + 37685051155 n^{12} - 365599182845 n^{10} + 2179449320620 n^{8} - 7671915416880 n^{6} + 14833923833664 n^{4} - 13751755969536 n^{2} + 4740548198400\right)}\]
\[\operatorname{Wg}([10]) = - \frac{4862}{n \left(n^{18} - 285 n^{16} + 32946 n^{14} - 1999370 n^{12} + 68943381 n^{10} - 1367593305 n^{8} + 15088541896 n^{6} - 84865562640 n^{4} + 202759531776 n^{2} - 131681894400\right)}\]