A052569 E.g.f. 1/((1-x)(1-x^3)).

1, 1, 2, 12, 48, 240, 2160, 15120, 120960, 1451520, 14515200, 159667200, 2395008000, 31135104000, 435891456000, 7846046208000, 125536739328000, 2134124568576000, 44816615940096000, 851515702861824000

Offset

0,3

Links

Robert Israel, Table of n, a(n) for n = 0..448

INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 512

Formula

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

Recurrence: {a(1)=1, a(0)=1, a(2)=2, (-14*n-n^3-7*n^2-8)*a(n)+(-2-n)*a(n+1)+a(n+3)-a(n+2)=0}

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

a(n) = n!*A008620(n). - R. J. Mathar, Nov 27 2011

Maple

spec := [S, {S=Prod(Sequence(Prod(Z, Z, Z)), Sequence(Z))}, labeled]: seq(combstruct[count](spec, size=n), n=0..20);
# Alternative:
f:= gfun:-rectoproc({ a(1)=1, a(0)=1, a(2)=2, (-14*n-n^3-7*n^2-8)*a(n)+(-2-n)*a(n+1)+a(n+3)-a(n+2)=0}, a(n), remember):
map(f, [$0..30]); # Robert Israel, Sep 25 2019

Mathematica

With[{nn=20}, CoefficientList[Series[1/((1-x)(1-x^3)), {x, 0, nn}], x]Range[0, nn]!] (* Harvey P. Dale, Aug 25 2012 *)

Crossrefs

Sequence in context: A333728 A354131 A370696 * A221663 A232663 A052591

Adjacent sequences: A052566 A052567 A052568 * A052570 A052571 A052572

Keyword

easy,nonn

Author

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

Status

approved