Weingarten functions for p = 3

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