A052583 E.g.f. x(1-x)/(1-x-x^2).

0, 1, 0, 6, 24, 240, 2160, 25200, 322560, 4717440, 76204800, 1357171200, 26345088000, 554204851200, 12553673932800, 304688127744000, 7887891787776000, 216969331138560000, 6319142847553536000

Offset

0,4

Links

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

INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 527

Formula

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

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

Sum(-1/5*(-3+4*_alpha)*_alpha^(-1-n), _alpha=RootOf(-1+_Z+_Z^2))*n!

a(n)=n!*A212804(n-1). - R. J. Mathar, Jun 03 2022

Maple

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

Mathematica

With[{nn=20}, CoefficientList[Series[x (1-x)/(1-x-x^2), {x, 0, nn}], x]Range[0, nn]!] (* Harvey P. Dale, Jul 24 2012 *)

Crossrefs

Sequence in context: A231317 A223105 A112675 * A052671 A052733 A323449

Adjacent sequences: A052580 A052581 A052582 * A052584 A052585 A052586

Keyword

easy,nonn

Author

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

Status

approved