A052627 E.g.f. (1-x)/(1-x-x^5).

1, 0, 0, 0, 0, 120, 720, 5040, 40320, 362880, 7257600, 119750400, 1916006400, 31135104000, 523069747200, 10461394944000, 230150688768000, 5335311421440000, 128047474114560000, 3162772610629632000

Offset: 0

Author

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

Keywords

• easy
• nonn

Links

• INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 573

Programs

Maple

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

Mathematica

With[{nn=20},CoefficientList[Series[(1-x)/(1-x-x^5),{x,0,nn}],x] Range[0,nn]!] (* Harvey P. Dale, Mar 12 2018 *)

Formula

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

Recurrence: {a(1)=0, a(0)=1, a(2)=0, a(4)=0, a(3)=0, (-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*(64+80*_alpha^4+100*_alpha^3+125*_alpha^2-689*_alpha)*_alpha^(-1-n), _alpha=RootOf(-1+_Z^5+_Z))*n!

a(n)=n!*A017899(n). - R. J. Mathar, Jun 03 2022