A052662 E.g.f. (1-x^2)/(1-2x-x^2+x^3).

1, 2, 8, 54, 480, 5400, 72720, 1144080, 20563200, 415860480, 9344160000, 230958604800, 6227499801600, 181909958630400, 5722470212659200, 192874123233792000, 6934147333521408000, 264875092391669760000

Offset: 0

Author

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

Keywords

• easy
• nonn

Links

• INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 609

Programs

Maple

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

Mathematica

With[{nn=20},CoefficientList[Series[(1-x^2)/(1-2x-x^2+x^3),{x,0,nn}],x] Range[ 0,nn]!] (* Harvey P. Dale, Jan 29 2023 *)

Formula

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

Recurrence: {a(0)=1, a(1)=2, a(2)=8, (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*(2+_alpha)*_alpha^(-1-n), _alpha=RootOf(_Z^3-_Z^2-2*_Z+1))*n!

a(n) = n!*A052534(n). - R. J. Mathar, Nov 27 2011