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

0,3

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..200

INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 580

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

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 *)

Crossrefs

Sequence in context: A196868 A077531 A214537 * A059944 A052139 A354019

Adjacent sequences: A052631 A052632 A052633 * A052635 A052636 A052637

Keyword

easy,nonn

Author

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

Status

approved