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

Author

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

Keywords

• easy
• nonn

Links

• INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 586

Programs

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 *)

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