A052625 E.g.f. (1-x)^2/(1-2x+x^2-x^3).

1, 0, 0, 6, 48, 360, 3600, 45360, 645120, 10160640, 177811200, 3432844800, 72329241600, 1650160512000, 40537905408000, 1067062284288000, 29961435119616000, 893842506805248000, 28234468042260480000

Offset: 0

Author

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

Keywords

• easy
• nonn

Links

• INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 571

Programs

Maple

spec := [S,{S=Sequence(Prod(Z,Z,Z,Sequence(Z),Sequence(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^3),{x,0,nn}], x]Range[0,nn]!] (* Harvey P. Dale, May 22 2012 *)

Formula

E.g.f.: -(-1+x)^2/(-1+2*x-x^2+x^3)

Recurrence: {a(1)=0, a(0)=1, a(2)=0, (-11*n-6-n^3-6*n^2)*a(n) +(n^2+5*n+6)*a(n+1) +(-2*n-6)*a(n+2) +a(n+3)=0}

Sum(-1/23*(2-11*_alpha+6*_alpha^2)*_alpha^(-1-n), _alpha=RootOf(-1+2*_Z-_Z^2+_Z^3))*n!

a(n) = (-1)^n*n!*A099529(n). - R. J. Mathar, Jun 03 2022