A052616 Expansion of e.g.f. (3+2*x)/(1-x^2).

3, 2, 6, 12, 72, 240, 2160, 10080, 120960, 725760, 10886400, 79833600, 1437004800, 12454041600, 261534873600, 2615348736000, 62768369664000, 711374856192000, 19207121117184000, 243290200817664000, 7298706024529920000, 102181884343418880000, 3372002183332823040000

Offset

0,1

Links

Table of n, a(n) for n=0..22.

INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 561.

Formula

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

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

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

a(n) = 3n! if n is even, 2n! otherwise.

a(n) = n!*A176059(n). - R. J. Mathar, Jun 03 2022

Sum_{n>=0} 1/a(n) = (5*e^2-1)/(12*e) = cosh(1)/3 + sinh(1)/2. - Amiram Eldar, Feb 02 2023

Maple

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

Mathematica

With[{nn=30}, CoefficientList[Series[(3+2x)/(1-x^2), {x, 0, nn}], x] Range[ 0, nn]!] (* Harvey P. Dale, Dec 12 2021 *)

Crossrefs

Cf. A176059.

Sequence in context: A188621 A175182 A291221 * A091461 A078091 A073883

Adjacent sequences: A052613 A052614 A052615 * A052617 A052618 A052619

Keyword

easy,nonn

Author

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

Status

approved