A052640 E.g.f. x*(1-x)/(1-2*x-x^2+x^3).

0, 1, 2, 18, 144, 1680, 22320, 352800, 6330240, 128096640, 2877638400, 71131737600, 1917922406400, 56024506137600, 1762396334899200, 59401108166400000, 2135568241078272000, 81575844571533312000

Offset

0,3

Links

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

INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 586

Formula

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

Recurrence: {a(1)=1, a(0)=0, a(2)=2, (n^3+6*n^2+11*n+6)*a(n)+(-n^2-5*n-6)*a(n+1)+(-2*n-6)*a(n+2)+a(n+3)=0}

Sum(1/7*(-_alpha+_alpha^2+1)*_alpha^(-1-n), _alpha=RootOf(_Z^3-_Z^2-2*_Z+1))*n!

a(n) = n!*A077998(n-1), n>0. - R. J. Mathar, Nov 27 2011

Maple

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

Mathematica

With[{nn=20}, CoefficientList[Series[-x*(-1+x)/(x^3-x^2-2*x+1), {x, 0, nn}], x] Range[0, nn]!] (* Harvey P. Dale, Oct 10 2023 *)

Crossrefs

Sequence in context: A220244 A001804 A277182 * A290215 A208654 A037565

Adjacent sequences: A052637 A052638 A052639 * A052641 A052642 A052643

Keyword

easy,nonn

Author

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

Status

approved