Weingarten functions for p = 6
Below are the values of the Weingarten function for permutation size p = 6. The input is given as a partition of p. You can also download them as a text file or as a python pickle file.
\[\operatorname{Wg}([1, 1, 1, 1, 1, 1]) = \frac{n^{8} - 41 n^{6} + 458 n^{4} - 1258 n^{2} + 240}{n^{14} - 56 n^{12} + 1078 n^{10} - 8668 n^{8} + 28721 n^{6} - 35476 n^{4} + 14400 n^{2}}\]
\[\operatorname{Wg}([2, 1, 1, 1, 1]) = \frac{- n^{4} + 24 n^{2} - 38}{n^{11} - 47 n^{9} + 655 n^{7} - 2773 n^{5} + 3764 n^{3} - 1600 n}\]
\[\operatorname{Wg}([3, 1, 1, 1]) = \frac{2 n^{6} - 51 n^{4} + 229 n^{2} - 60}{n^{14} - 56 n^{12} + 1078 n^{10} - 8668 n^{8} + 28721 n^{6} - 35476 n^{4} + 14400 n^{2}}\]
\[\operatorname{Wg}([2, 2, 1, 1]) = \frac{n^{4} - 3 n^{2} + 10}{n^{12} - 40 n^{10} + 438 n^{8} - 1660 n^{6} + 2161 n^{4} - 900 n^{2}}\]
\[\operatorname{Wg}([4, 1, 1]) = \frac{- 5 n^{2} + 13}{n^{11} - 40 n^{9} + 438 n^{7} - 1660 n^{5} + 2161 n^{3} - 900 n}\]
\[\operatorname{Wg}([3, 2, 1]) = \frac{- 2 n^{2} - 13}{n^{11} - 47 n^{9} + 655 n^{7} - 2773 n^{5} + 3764 n^{3} - 1600 n}\]
\[\operatorname{Wg}([5, 1]) = \frac{14 n^{2} - 140}{n^{12} - 55 n^{10} + 1023 n^{8} - 7645 n^{6} + 21076 n^{4} - 14400 n^{2}}\]
\[\operatorname{Wg}([2, 2, 2]) = \frac{- n^{4} - n^{2} - 358}{n^{13} - 56 n^{11} + 1078 n^{9} - 8668 n^{7} + 28721 n^{5} - 35476 n^{3} + 14400 n}\]
\[\operatorname{Wg}([4, 2]) = \frac{5 n^{4} + 75 n^{2} + 40}{n^{14} - 56 n^{12} + 1078 n^{10} - 8668 n^{8} + 28721 n^{6} - 35476 n^{4} + 14400 n^{2}}\]
\[\operatorname{Wg}([3, 3]) = \frac{4 n^{4} + 116 n^{2} - 360}{n^{14} - 56 n^{12} + 1078 n^{10} - 8668 n^{8} + 28721 n^{6} - 35476 n^{4} + 14400 n^{2}}\]
\[\operatorname{Wg}([6]) = - \frac{42}{n^{11} - 55 n^{9} + 1023 n^{7} - 7645 n^{5} + 21076 n^{3} - 14400 n}\]