A052653 E.g.f. (1-2x^2)/(1-x-2x^2).

1, 1, 2, 18, 120, 1320, 15120, 216720, 3427200, 62052480, 1237420800, 27263174400, 653837184000, 17005993804800, 476080648243200, 14283727121664000, 457058345103360000, 15540339420942336000

Offset

0,3

Links

Table of n, a(n) for n=0..17.

INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 600

Formula

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

Recurrence: {a(1)=1, a(0)=1, a(2)=2, (-2*n^2-6*n-4)*a(n)+(-2-n)*a(n+1)+a(n+2)=0}

Sum(-1/9*(-2+_alpha)*_alpha^(-1-n), _alpha=RootOf(-1+_Z+2*_Z^2))*n!

a(n) = n!*A001045(n), n>0. - R. J. Mathar, Nov 27 2011

Maple

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

Mathematica

With[{nn=20}, CoefficientList[Series[(1-2x^2)/(1-x-2x^2), {x, 0, nn}], x]Range[0, nn]!] (* Harvey P. Dale, Feb 13 2013 *)

Crossrefs

Sequence in context: A058052 A119578 A052610 * A342124 A289830 A361304

Adjacent sequences: A052650 A052651 A052652 * A052654 A052655 A052656

Keyword

easy,nonn

Author

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

Status

approved