A052599 Expansion of e.g.f.: 1/(1-2x-x^3).

1, 2, 8, 54, 480, 5280, 69840, 1078560, 19031040, 377758080, 8331724800, 202138675200, 5349968870400, 153396430387200, 4736570917478400, 156702542540544000, 5529893367398400000, 207341583834857472000

Offset: 0

Author

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

Keywords

• easy
• nonn

Links

• INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 544

Programs

Maple

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

Mathematica

With[{nn=20},CoefficientList[Series[1/(1-2x-x^3),{x,0,nn}],x] Range[0,nn]!] (* Harvey P. Dale, Apr 10 2022 *)

Formula

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

Recurrence: {a(0)=1, a(1)=2, a(2)=8, (-11*n-6-n^3-6*n^2)*a(n) +(-2*n-6)*a(n+2) +a(n+3)=0}

Sum(1/59*(16+12*_alpha^2+9*_alpha)*_alpha^(-1-n), _alpha=RootOf(-1+2*_Z+_Z^3))*n!

a(n) = n!*A008998(n). - R. J. Mathar, Nov 27 2011

Extensions

Definition clarified by Harvey P. Dale, Apr 10 2022