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

Author

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

Keywords

• easy
• nonn

Links

• INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 569

Programs

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 *)

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