A052659 Expansion of e.g.f. (1-2x)(1-x)/(1-4x+2x^2).

1, 1, 8, 84, 1152, 19680, 403200, 9636480, 263208960, 8087869440, 276137164800, 10370703974400, 424893579264000, 18858806481715200, 901431900123955200, 46165215285116928000, 2521886466187984896000

Offset

0,3

Links

Table of n, a(n) for n=0..16.

INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 606

Formula

E.g.f.: (-1+2*x)*(-1+x)/(1-4*x+2*x^2).

Recurrence: {a(1)=1, a(0)=1, a(2)=8, (2*n^2+6*n+4)*a(n)+(-4*n-8)*a(n+1)+a(n+2)=0}.

Sum(-1/4*(-1+2*_alpha)*_alpha^(-1-n), _alpha=RootOf(1-4*_Z+2*_Z^2))*n!.

a(n) = n!*A007070(n-1). - R. J. Mathar, Nov 27 2011

Maple

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

Crossrefs

Cf. A007070.

Sequence in context: A005797 A233835 A300993 * A346684 A350264 A113376

Adjacent sequences: A052656 A052657 A052658 * A052660 A052661 A052662

Keyword

easy,nonn

Author

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

Status

approved