A384368 Number of permutations of [2n] with n inversions.

1, 1, 5, 29, 174, 1068, 6655, 41926, 266338, 1703027, 10947079, 70673825, 457927079, 2976282415, 19395654894, 126688273871, 829176461458, 5436687172806, 35703722618623, 234807844921153, 1546217013188447, 10193761267335877, 67275841673522196, 444431529264364506

Offset: 0

Author

Alois P. Heinz, May 27 2025

Keywords

• nonn

Examples

			a(0) = 1: the empty permutation.
a(1) = 1: 21.
a(2) = 5: 1342, 1423, 2143, 2314, 3124.
a(3) = 29: 123654, 124563, 124635, 125364, 125436, 126345, 132564, 132645, 134265, 134526, 135246, 142365, 142536, 143256, 152346, 213564, 213645, 214365, 214536, 215346, 231465, 231546, 234156, 241356, 312465, 312546, 314256, 321456, 412356.
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..1208

Crossrefs

Cf. A008302, A128566.

Cf. A100220.

Programs

Maple

a:= n-> coeff(series(mul((1-q^j)/(1-q), j=1..2*n), q, n+1), q, n):
seq(a(n), n=0..23);

Formula

a(n) = A008302(2n,n).

a(n) ~ c * 3^(3*n - 1/2) / (sqrt(Pi*n) * 2^(2*n)), where c = QPochhammer(1/3) = A100220 = 0.5601260779279489449697922433141400143797363337983... - Vaclav Kotesovec, Jun 09 2025