Weingarten functions for p = 4

Below are the values of the Weingarten function for permutation size p = 4. The input is given as a partition of p. You can also download them as a text file or as a python pickle file. \[\operatorname{Wg}([1, 1, 1, 1]) = \frac{n^{4} - 8 n^{2} + 6}{n^{8} - 14 n^{6} + 49 n^{4} - 36 n^{2}}\] \[\operatorname{Wg}([2, 1, 1]) = - \frac{1}{n^{5} - 10 n^{3} + 9 n}\] \[\operatorname{Wg}([3, 1]) = \frac{2 n^{2} - 3}{n^{8} - 14 n^{6} + 49 n^{4} - 36 n^{2}}\] \[\operatorname{Wg}([2, 2]) = \frac{n^{2} + 6}{n^{8} - 14 n^{6} + 49 n^{4} - 36 n^{2}}\] \[\operatorname{Wg}([4]) = - \frac{5}{n^{7} - 14 n^{5} + 49 n^{3} - 36 n}\]