A363180 Number of permutations of [2n] with n parity changes.

1, 2, 8, 288, 10368, 1036800, 103680000, 20321280000, 3982970880000, 1290482565120000, 418116351098880000, 202368313931857920000, 97946263943019233280000, 66211674425481001697280000, 44759091911625157147361280000, 40283182720462641432625152000000

Offset: 0

Author

Alois P. Heinz, May 23 2023

Keywords

• nonn

Examples

			a(0) = 1: (), the empty permutation.
a(1) = 2: 12, 21.
a(2) = 8: 1243, 1423, 2134, 2314, 3241, 3421, 4132, 4312.
a(3) = 288: 123546, 123564, 124356, 124536, 125346, ..., 652431, 653241, 653421, 654213, 654231.
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..225

Crossrefs

Cf. A152874, A363236.

Programs

Maple

a:= proc(n) option remember; `if`(n<2, 2^n,
      (16*(n-2)^2*(2*n-1)*(n-1)^2*a(n-2)+4*(2*n^2-4*n+1)*a(n-1))/(2*n-3))
    end:
seq(a(n), n=0..18);

Formula

a(n) = A152874(2n,n).

From Vaclav Kotesovec, May 26 2023: (Start)

Recurrence: (2*n - 3)*a(n) = 4*(2*n^2 - 4*n + 1)*a(n-1) + 16*(n-2)^2*(n-1)^2*(2*n - 1)*a(n-2).

a(n) ~ 2^(2*n+1) * n^(2*n) / exp(2*n). (End)