A052557 Expansion of e.g.f. (1-x)/(1-x-x^3).

1, 0, 0, 6, 24, 120, 1440, 15120, 161280, 2177280, 32659200, 518918400, 9101030400, 174356582400, 3574309939200, 78460462080000, 1841205510144000, 45883678224384000, 1210048630382592000

Offset

0,4

Links

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

INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 499

Formula

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

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

a(n) = Sum(-1/31*(2+3*_alpha^2-11*_alpha)*_alpha^(-1-n), _alpha=RootOf(-1+_Z+_Z^3))*n!.

a(n) = n!*A078012(n). - R. J. Mathar, Nov 27 2011

Maple

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

Mathematica

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

Prog

(PARI) my(x='x+O('x^30)); Vec(serlaplace( (1-x)/(1-x-x^3) )) \\ G. C. Greubel, May 07 2019
(Magma) m:=30; R<x>:=PowerSeriesRing(Rationals(), m); b:=Coefficients(R!( (1-x)/(1-x-x^3) )); [Factorial(n-1)*b[n]: n in [1..m]]; // G. C. Greubel, May 07 2019
(Sage)
R = PowerSeriesRing(QQ, 'x')
x = R.gen().O(30)
T = (1-x)/(1-x-x^3)
list(T.egf_to_ogf())
# G. C. Greubel, May 07 2019
(GAP) a:=[0, 0, 6];; 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: A293123 A355575 A060249 * A357192 A357194 A188232

Adjacent sequences: A052554 A052555 A052556 * A052558 A052559 A052560

Keyword

easy,nonn

Author

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

Status

approved