A179564 Number of permutations of [n] with the number moved left exceeding the number moved right by 3.

0, 0, 0, 0, 1, 6, 134, 960, 16615, 138022, 2425600, 23279224, 444500577, 4880181294, 102914967458, 1277238809792, 29767443364523, 412889949481670, 10588965173821348, 162515224089696984, 4560137456338593333, 76773519570724122126, 2343258977445039475014

Offset

1,6

Links

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

Formula

a(n) = Sum_{e=0..floor((n+3)/2)} binomial(n,2*e-3) * A271697(2*e-3,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+3)\2, binomial(n, 2*e-3)*a271697(2*e-3, e)); \\ Seiichi Manyama, Apr 23 2026

Crossrefs

Column k=3 (or k=-3) of A062866.

Equal number moved left and right, see A062868.

Cf. A046739, A271697.

Sequence in context: A129047 A209276 A244745 * A263583 A295408 A301463

Adjacent sequences: A179561 A179562 A179563 * A179565 A179566 A179567

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