A382309 Number of permutations of [2n] with exactly n ascents and an even number of inversions.
1, 1, 5, 147, 7819, 655315, 81255642, 13985577438, 3191399514435, 932692830330915, 339781108888268398, 150979116192562395562, 80377829037419610855326, 50509994170589416909171726, 36995186973806250851237265812, 31240798437883511927927569474140
Offset: 0
Keywords
Links
- Alois P. Heinz, Table of n, a(n) for n = 0..225
- Wikipedia, Inversion
- Wikipedia, Permutation
Formula
a(n) = A128612(2n,n).
a(n) ~ sqrt(3) * 2^(2*n) * n^(2*n) / exp(2*n). - Vaclav Kotesovec, Apr 02 2025