A052613 E.g.f. (1-2x)/(1-2x-x^2+x^3).

1, 0, 2, 6, 72, 720, 10080, 156240, 2822400, 56972160, 1280966400, 31654022400, 853580851200, 24932991283200, 784343085926400, 26435945023488000, 950417730662400000, 36304660098330624000, 1468365202287599616000

Offset: 0

Author

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

Keywords

• easy
• nonn

Links

• INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 558

Programs

Maple

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

Mathematica

With[{nn=20},CoefficientList[Series[(1-2x)/(1-2x-x^2+x^3),{x,0,nn}],x] Range[0,nn]!] (* Harvey P. Dale, Dec 08 2015 *)

Formula

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

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

a(n)=n!*A077998(n-2), n>=2. - R. J. Mathar, Jun 03 2022