Weingarten functions for p = 2

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