A169934 Number of permutations of [n] with the number moved left exceeding the number moved right by 2.

0, 0, 0, 1, 5, 66, 392, 4859, 34659, 482272, 4099634, 65762489, 653977909, 12026621478, 137361430156, 2862534403223, 36968414699239, 862935261673212, 12440701298168534, 321935664074780549, 5126628962937663529, 145768013651370381026, 2541561479354892816304

Offset

1,5

Links

Seiichi Manyama, Table of n, a(n) for n = 1..450

Formula

a(n) = Sum_{e=0..floor((n+2)/2)} binomial(n,2*e-2) * A271697(2*e-2,e). - Seiichi Manyama, Apr 23 2026

Prog

(PARI) E(n, k) = sum(j=0, k, (-1)^j*binomial(n+1, j)*(k+1-j)^n);
a271697(n, k) = sum(j=0, n, (-1)^(n-j)*binomial(n, j)*E(j, k));
a(n) = sum(e=0, (n+2)\2, binomial(n, 2*e-2)*a271697(2*e-2, e)); \\ Seiichi Manyama, Apr 23 2026

Crossrefs

Column k=2 (or k=-2) of A062866.

Equal number moved left and right, see A062868.

Cf. A046739, A271697.

Sequence in context: A263784 A263785 A263786 * A162443 A219678 A297743

Adjacent sequences: A169931 A169932 A169933 * A169935 A169936 A169937

Keyword

nonn

Author

R. H. Hardin, Jul 19 2010

Extensions

a(19)-a(20) from Alois P. Heinz, Jul 31 2018

a(21)-a(23) from Alois P. Heinz, Apr 28 2024

Status

approved