Weingarten functions for p = 7
Below are the values of the Weingarten function for permutation size p = 7. The input is given as a partition of p. You can also download them as a text file or as a python pickle file.
\[\operatorname{Wg}([1, 1, 1, 1, 1, 1, 1]) = \frac{n^{8} - 71 n^{6} + 1568 n^{4} - 11398 n^{2} + 15780}{n \left(n^{14} - 92 n^{12} + 3094 n^{10} - 47476 n^{8} + 340769 n^{6} - 1069432 n^{4} + 1291536 n^{2} - 518400\right)}\]
\[\operatorname{Wg}([2, 1, 1, 1, 1, 1]) = \frac{- n^{8} + 61 n^{6} - 1058 n^{4} + 4958 n^{2} - 1440}{n^{2} \left(n^{14} - 92 n^{12} + 3094 n^{10} - 47476 n^{8} + 340769 n^{6} - 1069432 n^{4} + 1291536 n^{2} - 518400\right)}\]
\[\operatorname{Wg}([3, 1, 1, 1, 1]) = \frac{2 n^{6} - 102 n^{4} + 1288 n^{2} - 2868}{n \left(n^{14} - 92 n^{12} + 3094 n^{10} - 47476 n^{8} + 340769 n^{6} - 1069432 n^{4} + 1291536 n^{2} - 518400\right)}\]
\[\operatorname{Wg}([2, 2, 1, 1, 1]) = \frac{n^{6} - 45 n^{4} + 488 n^{2} - 1284}{n \left(n^{14} - 92 n^{12} + 3094 n^{10} - 47476 n^{8} + 340769 n^{6} - 1069432 n^{4} + 1291536 n^{2} - 518400\right)}\]
\[\operatorname{Wg}([4, 1, 1, 1]) = \frac{- 5 n^{6} + 207 n^{4} - 1762 n^{2} + 720}{n^{2} \left(n^{14} - 92 n^{12} + 3094 n^{10} - 47476 n^{8} + 340769 n^{6} - 1069432 n^{4} + 1291536 n^{2} - 518400\right)}\]
\[\operatorname{Wg}([3, 2, 1, 1]) = - \frac{2}{n^{10} - 66 n^{8} + 1353 n^{6} - 10648 n^{4} + 30096 n^{2} - 20736}\]
\[\operatorname{Wg}([5, 1, 1]) = \frac{14 n^{2} - 84}{n \left(n^{12} - 67 n^{10} + 1419 n^{8} - 12001 n^{6} + 40744 n^{4} - 50832 n^{2} + 20736\right)}\]
\[\operatorname{Wg}([2, 2, 2, 1]) = \frac{- n^{6} + 23 n^{4} - 382 n^{2} + 2880}{n^{2} \left(n^{14} - 92 n^{12} + 3094 n^{10} - 47476 n^{8} + 340769 n^{6} - 1069432 n^{4} + 1291536 n^{2} - 518400\right)}\]
\[\operatorname{Wg}([4, 2, 1]) = \frac{5 n^{2} + 51}{n \left(n^{12} - 76 n^{10} + 1878 n^{8} - 17428 n^{6} + 61921 n^{4} - 78696 n^{2} + 32400\right)}\]
\[\operatorname{Wg}([3, 3, 1]) = \frac{4 n^{4} + 32 n^{2} - 1716}{n \left(n^{14} - 92 n^{12} + 3094 n^{10} - 47476 n^{8} + 340769 n^{6} - 1069432 n^{4} + 1291536 n^{2} - 518400\right)}\]
\[\operatorname{Wg}([6, 1]) = \frac{- 42 n^{2} + 720}{n^{2} \left(n^{12} - 91 n^{10} + 3003 n^{8} - 44473 n^{6} + 296296 n^{4} - 773136 n^{2} + 518400\right)}\]
\[\operatorname{Wg}([3, 2, 2]) = \frac{2 n^{4} + 10 n^{2} + 1668}{n \left(n^{14} - 92 n^{12} + 3094 n^{10} - 47476 n^{8} + 340769 n^{6} - 1069432 n^{4} + 1291536 n^{2} - 518400\right)}\]
\[\operatorname{Wg}([5, 2]) = \frac{- 14 n^{4} - 226 n^{2} - 1440}{n^{2} \left(n^{14} - 92 n^{12} + 3094 n^{10} - 47476 n^{8} + 340769 n^{6} - 1069432 n^{4} + 1291536 n^{2} - 518400\right)}\]
\[\operatorname{Wg}([4, 3]) = \frac{- 10 n^{4} - 470 n^{2} + 2160}{n^{2} \left(n^{14} - 92 n^{12} + 3094 n^{10} - 47476 n^{8} + 340769 n^{6} - 1069432 n^{4} + 1291536 n^{2} - 518400\right)}\]
\[\operatorname{Wg}([7]) = \frac{132}{n \left(n^{12} - 91 n^{10} + 3003 n^{8} - 44473 n^{6} + 296296 n^{4} - 773136 n^{2} + 518400\right)}\]