A052556 Expansion of e.g.f. 1/(1-x-x^3).

1, 1, 2, 12, 72, 480, 4320, 45360, 524160, 6894720, 101606400, 1636588800, 28740096000, 547977830400, 11245999564800, 247150455552000, 5795612798976000, 144409095806976000, 3809412354908160000

Offset

0,3

Links

G. C. Greubel, Table of n, a(n) for n = 0..420

INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 497

Formula

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

a(n) = n*a(n-1) + n*(n-1)*(n-2)*a(n-3), with a(0)=1, a(1)=1, a(2)=2.

a(n) = Sum(1/31*(4+6*_alpha^2+9*_alpha)*_alpha^(-1-n), _alpha=RootOf(-1+_Z+_Z^3))*n!.

a(n) = n! * A000930(n). - R. J. Mathar, Nov 27 2011

Maple

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

Mathematica

With[{nn=30}, CoefficientList[Series[1/(1-x-x^3), {x, 0, nn}], x]* Range[0, nn]!] (* G. C. Greubel, May 01 2017 *)

Prog

(PARI) x='x+O('x^30); Vec(serlaplace( 1/(1-x-x^3) )) \\ G. C. Greubel, May 01 2017
(Magma) m:=30; R<x>:=PowerSeriesRing(Rationals(), m); b:=Coefficients(R!( 1/(1-x-x^3) )); [Factorial(n-1)*b[n]: n in [1..m]]; // G. C. Greubel, May 07 2019
(Sage) m = 30; T = taylor(1/(1-x-x^3), x, 0, m); [factorial(n)*T.coefficient(x, n) for n in (0..m)] # G. C. Greubel, May 07 2019
(GAP) a:=[1, 2, 12];; for n in [4..30] do a[n]:=n*a[n-1]+n*(n-1)*(n-2) *a[n-3]; od; Concatenation([1], a); # G. C. Greubel, May 07 2019

Crossrefs

Sequence in context: A018931 A062119 A181966 * A371039 A052833 A277490

Adjacent sequences: A052553 A052554 A052555 * A052557 A052558 A052559

Keyword

easy,nonn

Author

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

Status

approved