A052575 Expansion of e.g.f. (1-x)/(1-2*x-2*x^2+2*x^3).

1, 1, 8, 48, 528, 6240, 95040, 1632960, 32578560, 725760000, 18027878400, 491774976000, 14645952921600, 472356889804800, 16409046682828800, 610694391250944000, 24244324628299776000, 1022626965270822912000

Offset: 0

Author

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

Keywords

• easy
• nonn

Links

• Robert Israel, Table of n, a(n) for n = 0..390
• INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 518.

Crossrefs

Cf. A052528.

Programs

Maple

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

Mathematica

m = 17; Range[0, m]! * CoefficientList[Series[(1 - x)/(1 - 2*x - 2*x^2 + 2*x^3), {x, 0, m}], x] (* Amiram Eldar, Mar 07 2022 *)

PARI

my(x='x+O('x^25)); Vec(serlaplace((1-x)/(1-2*x-2*x^2+2*x^3))) \\ Michel Marcus, Mar 07 2022

Formula

E.g.f.: (1-x)/(1-2*x-2*x^2+2*x^3).

(12+2*n^3+12*n^2+22*n)*a(n) + (-2*n^2-10*n-12)*a(n+1) + (-2*n-6)*a(n+2) + a(n+3) = 0, with a(1)=1, a(0)=1, a(2)=8.

Sum_(-1/37*(-5+9*_alpha^2-12*_alpha)*_alpha^(-1-n), _alpha=RootOf(2*_Z^3-2*_Z^2-2*_Z+1))*n!.

a(n) = n!*A052528(n). - R. J. Mathar, Nov 27 2011