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

Author

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

Keywords

• easy
• nonn

Links

• INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 568

Programs

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 *)

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