A052623 E.g.f. x(1-x)^2/(1-3x+x^2).

0, 1, 2, 18, 192, 2520, 39600, 725760, 15200640, 358162560, 9376819200, 270037152000, 8483597337600, 288734500454400, 10582834303641600, 415593298568448000, 17408598098411520000, 774797125808369664000

Offset

0,3

Links

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

INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 569

Formula

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

Recurrence: {a(1)=1, a(0)=0, a(2)=2, (n^2+3*n+2)*a(n)+(-6-3*n)*a(n+1)+a(n+2)=0, a(3)=18}

Sum(-1/5*(-3+7*_alpha)*_alpha^(-1-n), _alpha=RootOf(_Z^2-3*_Z+1))*n!

a(n)=n!*A088305(n-1). - R. J. Mathar, Jun 03 2022

Maple

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

Mathematica

With[{nn=20}, CoefficientList[Series[x (1-x)^2/(1-3x+x^2), {x, 0, nn}], x] Range[ 0, nn]!] (* Harvey P. Dale, May 30 2021 *)

Crossrefs

Sequence in context: A362731 A138413 A066274 * A362992 A155542 A157765

Adjacent sequences: A052620 A052621 A052622 * A052624 A052625 A052626

Keyword

easy,nonn

Author

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

Status

approved