A052614 E.g.f. 1/((1-x)(1-x^4)).

1, 1, 2, 6, 48, 240, 1440, 10080, 120960, 1088640, 10886400, 119750400, 1916006400, 24908083200, 348713164800, 5230697472000, 104613949440000, 1778437140480000, 32011868528640000, 608225502044160000

Offset: 0

Author

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

Keywords

• easy
• nonn

Links

• INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 559

Programs

Maple

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

Mathematica

With[{nn=20},CoefficientList[Series[1/((1-x)(1-x^4)),{x,0,nn}],x] Range[0,nn]!] (* Harvey P. Dale, Jul 30 2013 *)

Formula

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

Recurrence: {a(1)=1, a(0)=1, a(3)=6, a(2)=2, (-61*n-11*n^3-n^4-30-41*n^2)*a(n) +(-n^2-5*n-6)*a(n+1) +(-n-3)*a(n+2) +a(n+4) -a(n+3)=0}

(Sum(1/16*(2*_alpha+_alpha^2-1)*_alpha^(-1-n), _alpha=RootOf(1+_Z+_Z^2+_Z^3))+1/4*n+5/8)*n!

n!*[n/4+1].

a(n)=n!*A008621(n). - R. J. Mathar, Jun 03 2022