A052632 E.g.f. 1/(1-x-x^5).

1, 1, 2, 6, 24, 240, 2160, 20160, 201600, 2177280, 29030400, 439084800, 7185024000, 124540416000, 2266635571200, 44460928512000, 941525544960000, 21341245685760000, 512189896458240000

Offset: 0

Author

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

Keywords

• easy
• nonn

Links

• INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 578

Programs

Maple

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

Mathematica

With[{nn=20},CoefficientList[Series[1/(1-x-x^5),{x,0,nn}],x] Range[0,nn]!] (* Harvey P. Dale, Sep 13 2019 *)

Formula

E.g.f.: -1/(-1+x^5+x)

D-finite Recurrence: {a(1)=1, a(0)=1, a(3)=6, a(2)=2, a(4)=24, (-n^5-15*n^4-274*n-120-85*n^3-225*n^2)*a(n) +(-5-n)*a(n+4) +a(n+5)=0}

Sum(1/3381*(256+320*_alpha^4+400*_alpha^3+500*_alpha^2+625*_alpha)*_alpha^(-1-n), _alpha=RootOf(-1+_Z^5+_Z))*n!

a(n)=n!*A003520(n). - R. J. Mathar, Jun 03 2022