A052586 Expansion of e.g.f.: (1-x^3)/(1-x-x^3).

1, 1, 2, 6, 48, 360, 2880, 30240, 362880, 4717440, 68947200, 1117670400, 19639065600, 373621248000, 7671689625600, 168689993472000, 3954407288832000, 98525417582592000, 2599363724525568000

Offset

0,3

Links

Table of n, a(n) for n=0..18.

INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 531

Formula

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

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

Sum(1/31*(-2*_alpha+9*_alpha^2+6)*_alpha^(-1-n), _alpha=RootOf(-1+_Z+_Z^3))*n!

a(n)=n!*A000930(n-1),n>0. - R. J. Mathar, Jun 03 2022

Maple

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

Mathematica

With[{nn=20}, CoefficientList[Series[(1-x^3)/(1-x-x^3), {x, 0, nn}], x] Range[0, nn]!] (* Harvey P. Dale, Nov 07 2020 *)

Crossrefs

Sequence in context: A239836 A052593 A358065 * A052554 A228159 A249786

Adjacent sequences: A052583 A052584 A052585 * A052587 A052588 A052589

Keyword

easy,nonn

Author

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

Extensions

Definition clarified by Harvey P. Dale, Nov 07 2020

Status

approved