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

%I A052627 #15 Jun 03 2022 18:38:43
%S A052627 1,0,0,0,0,120,720,5040,40320,362880,7257600,119750400,1916006400,
%T A052627 31135104000,523069747200,10461394944000,230150688768000,
%U A052627 5335311421440000,128047474114560000,3162772610629632000
%N A052627 E.g.f. (1-x)/(1-x-x^5).
%H A052627 INRIA Algorithms Project, <a href="http://ecs.inria.fr/services/structure?nbr=573">Encyclopedia of Combinatorial Structures 573</a>
%F A052627 E.g.f.: (-1+x)/(-1+x^5+x)
%F A052627 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}
%F A052627 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!
%F A052627 a(n)=n!*A017899(n). - _R. J. Mathar_, Jun 03 2022
%p A052627 spec := [S,{S=Sequence(Prod(Z,Z,Z,Z,Z,Sequence(Z)))},labeled]: seq(combstruct[count](spec,size=n), n=0..20);
%t A052627 With[{nn=20},CoefficientList[Series[(1-x)/(1-x-x^5),{x,0,nn}],x] Range[0,nn]!] (* _Harvey P. Dale_, Mar 12 2018 *)
%K A052627 easy,nonn
%O A052627 0,6
%A A052627 encyclopedia(AT)pommard.inria.fr, Jan 25 2000