A179565 Number of permutations of [n] with the number moved left exceeding the number moved right by 4.

0, 0, 0, 0, 0, 1, 7, 267, 2235, 53830, 511412, 11370998, 122063526, 2787148807, 33618432005, 817366315013, 10992904020133, 288039183533356, 4284317049630762, 121306011298119784, 1980129988160763368, 60512049675634245013, 1076468156084116242851

Offset

1,7

Links

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

Formula

a(n) = Sum_{e=0..floor((n+4)/2)} binomial(n,2*e-4) * A271697(2*e-4,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+4)\2, binomial(n, 2*e-4)*a271697(2*e-4, e)); \\ Seiichi Manyama, Apr 23 2026

Crossrefs

Column k=4 (or k=-4) of A062866.

Equal number moved left and right, see A062868.

Cf. A046739, A271697.

Sequence in context: A231486 A048291 A015089 * A069449 A100465 A140031

Adjacent sequences: A179562 A179563 A179564 * A179566 A179567 A179568

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