A052621 E.g.f. (2+x+x^2+x^3)/(1-x^4).

2, 1, 2, 6, 48, 120, 720, 5040, 80640, 362880, 3628800, 39916800, 958003200, 6227020800, 87178291200, 1307674368000, 41845579776000, 355687428096000, 6402373705728000, 121645100408832000, 4865804016353280000

Offset: 0

Author

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

Keywords

• easy
• nonn

Links

• INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 567

Programs

Maple

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

Mathematica

With[{nn=20},CoefficientList[Series[(2+x+x^2+x^3)/(1-x^4),{x,0,nn}],x] Range[0,nn]!] (* Harvey P. Dale, Oct 10 2023 *)

Formula

E.g.f.: -(x^3+x^2+x+2)/(-1+x^4)

Recurrence: {a(1)=1, a(3)=6, a(2)=2, a(0)=2, (-n^4-35*n^2-50*n-24-10*n^3)*a(n)+a(n+4)=0}

Sum(1/4*(_alpha^3+_alpha^2+2*_alpha+1)*_alpha^(-1-n), _alpha=RootOf(-1+_Z^4))*n!

2n! if n is 0 mod 4, n! otherwise.

a(n)=n!*A177704(n+3). - R. J. Mathar, Jun 03 2022