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

0,1

Links

Table of n, a(n) for n=0..20.

INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 523

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

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 *)

Crossrefs

Sequence in context: A320834 A355932 A342463 * A266314 A153908 A048296

Adjacent sequences: A052576 A052577 A052578 * A052580 A052581 A052582

Keyword

easy,nonn

Author

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

Status

approved