A052634 Expansion of e.g.f. 1/((1-2*x^2)*(1-x)).

1, 1, 6, 18, 168, 840, 10800, 75600, 1249920, 11249280, 228614400, 2514758400, 60833203200, 790831641600, 22230464256000, 333456963840000, 10691545632768000, 181756275757056000, 6549628300959744000

Offset: 0

Author

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

Keywords

• easy
• nonn

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..200
• INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 580

Programs

Maple

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

Mathematica

With[{nn=20},CoefficientList[Series[1/((1-2x^2)(1-x)),{x,0,nn}],x] Range[0,nn]!] (* Harvey P. Dale, Aug 13 2014 *)

Formula

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

Recurrence: {a(1)=1, a(0)=1, a(2)=6, (12+2*n^3+12*n^2+22*n)*a(n) +(-2*n^2-10*n-12)*a(n+1) +(-n-3)*a(n+2) +a(n+3)=0}.

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

a(n) = n!*[2^floor(n/2+1)-1].

a(n)=n!*A052551(n). - R. J. Mathar, Jun 03 2022