A052636 Expansion of e.g.f. (2-x-2x^2)/((1-x)(1-2x^2)).

2, 1, 6, 6, 120, 120, 6480, 5040, 685440, 362880, 119750400, 39916800, 31135104000, 6227020800, 11245999564800, 1307674368000, 5377157001216000, 355687428096000, 3284417711038464000

Offset

0,1

Links

Table of n, a(n) for n=0..18.

INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 582

Formula

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

D-finite Recurrence: {a(1)=1, a(2)=6, a(0)=2, (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}

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

n!*[2^(n/2)+1] if n is even, n! otherwise.

a(n) = n!*A052552(n). - R. J. Mathar, Jun 03 2022

Maple

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

Mathematica

With[{nn=20}, CoefficientList[Series[(2-x-2x^2)/((1-x)(1-2x^2)), {x, 0, nn}], x] Range[0, nn]!] (* Harvey P. Dale, Sep 16 2016 *)

Crossrefs

Cf. A052552.

Sequence in context: A053442 A019082 A345323 * A172430 A325139 A084312

Adjacent sequences: A052633 A052634 A052635 * A052637 A052638 A052639

Keyword

easy,nonn

Author

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

Status

approved