%I #15 Jun 03 2022 18:49:12

%S 1,1,2,6,48,240,1440,10080,120960,1088640,10886400,119750400,

%T 1916006400,24908083200,348713164800,5230697472000,104613949440000,

%U 1778437140480000,32011868528640000,608225502044160000

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

%H INRIA Algorithms Project, <a href="http://ecs.inria.fr/services/structure?nbr=559">Encyclopedia of Combinatorial Structures 559</a>

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

%F 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}

%F (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!

%F n!*[n/4+1].

%F a(n)=n!*A008621(n). - _R. J. Mathar_, Jun 03 2022

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

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

%K easy,nonn

%O 0,3

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