A052622 E.g.f. (1-x^2)/(1-2x-x^2).

1, 2, 8, 60, 576, 6960, 100800, 1703520, 32901120, 714873600, 17258572800, 458324697600, 13277924352000, 416724685977600, 14084873439436800, 510058387238400000, 19702238017093632000, 808611973910028288000

Offset

0,2

Links

Table of n, a(n) for n=0..17.

INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 568

Formula

E.g.f.: (-1+x^2)/(-1+2*x+x^2)

Recurrence: {a(0)=1, a(1)=2, a(2)=8, (-2-n^2-3*n)*a(n) +(-4-2*n)*a(n+1) +a(n+2)=0}

Sum(-1/2*(-1+_alpha)*_alpha^(-1-n), _alpha=RootOf(-1+2*_Z+_Z^2))*n!

a(n) = n!*((1+sqrt(2))^n - (1-sqrt(2))^n)/sqrt(2). - Vaclav Kotesovec, Oct 05 2013

a(n)=n!*A052542(n). - R. J. Mathar, Jun 03 2022

Maple

spec := [S, {S=Sequence(Prod(Union(Z, Z), Sequence(Prod(Z, Z))))}, labeled]: seq(combstruct[count](spec, size=n), n=0..20);

Mathematica

With[{nn=20}, CoefficientList[Series[(1-x^2)/(1-2x-x^2), {x, 0, nn}], x]Range[0, nn]!] (* Harvey P. Dale, Mar 04 2013 *)

Crossrefs

Sequence in context: A053871 A364395 A208124 * A303672 A303062 A001188

Adjacent sequences: A052619 A052620 A052621 * A052623 A052624 A052625

Keyword

easy,nonn

Author

encyclopedia(AT)pommard.inria.fr, Jan 25 2000

Status

approved