A052600 Expansion of e.g.f. 1/((1-2*x)*(1-x^2)).

1, 2, 10, 60, 504, 5040, 61200, 856800, 13749120, 247484160, 4953312000, 108972864000, 2615827737600, 68011521177600, 1904409771264000, 57132293137920000, 1828254303203328000, 62160646308913152000

Offset

0,2

Links

G. C. Greubel, Table of n, a(n) for n = 0..400

INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 545

Formula

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

Recurrence: {a(0)=1, a(1)=2, a(2)=10, (12+2*n^3+12*n^2+22*n)*a(n) +(-n^2-5*n-6)*a(n+1) +(-2*n-6)*a(n+2) +a(n+3)=0}.

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

a(n) = (4*2^n-1)/3*n! if n is even, a(n) = (4*2^n-2)/3*n! otherwise.

a(n) = n!*A000975(n+1). - R. J. Mathar

Maple

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

Mathematica

With[{nn=20}, CoefficientList[Series[1/((1-2x)(1-x^2)), {x, 0, nn}], x]Range[0, nn]!] (* Harvey P. Dale, Jan 21 2013 *)

Prog

(PARI) x='x+O('x^50); Vec(serlaplace(1/((1-2*x)*(1-x^2)))) \\ G. C. Greubel, Oct 11 2017

Crossrefs

Cf. A000975.

Sequence in context: A290446 A350225 A277472 * A183958 A356343 A352277

Adjacent sequences: A052597 A052598 A052599 * A052601 A052602 A052603

Keyword

easy,nonn

Author

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

Status

approved