A052580 E.g.f. (1-2x)/(1-2x-x^2).

1, 0, 2, 12, 120, 1440, 20880, 352800, 6814080, 148055040, 3574368000, 94922150400, 2749948185600, 86306508288000, 2917072801843200, 105636550795776000, 4080467097907200000, 167469023145295872000

Offset: 0

Author

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

Keywords

• easy
• nonn

Links

• INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 524

Programs

Maple

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

Mathematica

With[{nn=20},CoefficientList[Series[(1-2x)/(1-2x-x^2),{x,0,nn}],x] Range[ 0,nn]!] (* Harvey P. Dale, Dec 05 2018 *)

Formula

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

D-finite recurrence: {a(1)=0, a(0)=1, (-2-n^2-3*n)*a(n)+(-4-2*n)*a(n+1)+a(n+2)=0.}

Sum(1/4*(-1+3*_alpha)*_alpha^(-1-n), _alpha=RootOf(-1+2*_Z+_Z^2))*n!

a(n) = n!*A000129(n-1). - R. J. Mathar, Nov 27 2011