A052579 E.g.f. (2+x+x^2)/((1-x)(1+x+x^2)).

2, 1, 2, 12, 24, 120, 1440, 5040, 40320, 725760, 3628800, 39916800, 958003200, 6227020800, 87178291200, 2615348736000, 20922789888000, 355687428096000, 12804747411456000, 121645100408832000, 2432902008176640000

Offset: 0

Author

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

Keywords

• easy
• nonn

Links

• INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 523

Programs

Maple

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

Mathematica

With[{nn=20},CoefficientList[Series[(2+x+x^2)/((1-x)(1+x+x^2)),{x,0,nn}],x] Range[0,nn]!] (* Harvey P. Dale, May 10 2019 *)

Formula

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

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

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

a(n) = n!*A131534(n+1). - R. J. Mathar, Nov 27 2011