Weingarten functions for p = 5

Below are the values of the Weingarten function for permutation size p = 5. The input is given as a partition of p. You can also download them as a text file or as a python pickle file. \[\operatorname{Wg}([1, 1, 1, 1, 1]) = \frac{n^{4} - 20 n^{2} + 78}{n^{9} - 30 n^{7} + 273 n^{5} - 820 n^{3} + 576 n}\] \[\operatorname{Wg}([2, 1, 1, 1]) = \frac{- n^{4} + 14 n^{2} - 24}{n^{10} - 30 n^{8} + 273 n^{6} - 820 n^{4} + 576 n^{2}}\] \[\operatorname{Wg}([3, 1, 1]) = \frac{2}{n^{7} - 21 n^{5} + 84 n^{3} - 64 n}\] \[\operatorname{Wg}([2, 2, 1]) = \frac{n^{2} - 2}{n^{9} - 30 n^{7} + 273 n^{5} - 820 n^{3} + 576 n}\] \[\operatorname{Wg}([4, 1]) = \frac{- 5 n^{2} + 24}{n^{10} - 30 n^{8} + 273 n^{6} - 820 n^{4} + 576 n^{2}}\] \[\operatorname{Wg}([3, 2]) = \frac{- 2 n^{2} - 24}{n^{10} - 30 n^{8} + 273 n^{6} - 820 n^{4} + 576 n^{2}}\] \[\operatorname{Wg}([5]) = \frac{14}{n^{9} - 30 n^{7} + 273 n^{5} - 820 n^{3} + 576 n}\]