A052581 E.g.f. (1-x)/(1-x-x^4).

1, 0, 0, 0, 24, 120, 720, 5040, 80640, 1088640, 14515200, 199584000, 3353011200, 62270208000, 1220496076800, 24845812992000, 543992537088000, 12804747411456000, 320118685286400000, 8393511928209408000

Offset: 0

Author

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

Keywords

• easy
• nonn

Comments

Except for an initial 1, this is the p-INVERT of (1,1,1,1,1,...) for p(S) = (1 - S)(1 - 2 S); see A291000. - Clark Kimberling, Aug 24 2017

Links

• INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 525

Programs

Maple

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

Mathematica

With[{nn=20},CoefficientList[Series[(1-x)/(1-x-x^4),{x,0,nn}],x] Range[0,nn]!] (* Harvey P. Dale, Sep 27 2016 *)

Formula

E.g.f.: (-1+x)/(-1+x^4+x)

Recurrence: {a(1)=0, a(0)=1, a(2)=0, a(3)=0, (-n^4-35*n^2-50*n-24-10*n^3)*a(n) +(-n-4)*a(n+3) +a(n+4)=0}

Sum(-1/283*(9+12*_alpha^3+16*_alpha^2-73*_alpha)*_alpha^(-1-n), _alpha=RootOf(-1+_Z^4+_Z))*n!

a(n)= n!*A017898(n). - R. J. Mathar, Nov 27 2011