%I #22 Apr 18 2017 07:03:58

%S 1,0,0,6,48,120,1440,25200,282240,2903040,50803200,958003200,

%T 16286054400,305124019200,6887085004800,160843947264000,

%U 3807947759616000,98169730154496000,2746618319757312000

%N E.g.f. (1-x)/(1-x-x^3-x^4+x^5).

%H Vincenzo Librandi, <a href="/A052651/b052651.txt">Table of n, a(n) for n = 0..200</a>

%H INRIA Algorithms Project, <a href="http://ecs.inria.fr/services/structure?nbr=598">Encyclopedia of Combinatorial Structures 598</a>

%F E.g.f.: (1-x)/(1-x-x^4+x^5-x^3)

%F Recurrence: {a(1)=0, a(0)=1, a(2)=0, a(3)=6, a(4)=48, (n^5+15*n^4+274*n+120+85*n^3+225*n^2)*a(n)+(-14*n^3-71*n^2-154*n-120-n^4)*a(n+1)+(-12*n^2-47*n-60-n^3)*a(n+2)+(-5-n)*a(n+4)+a(n+5)=0}

%F Sum(1/8519*(138+2003*_alpha-346*_alpha^2-444*_alpha^3+11*_alpha^4)*_alpha^(-1-n), _alpha=RootOf(1-_Z-_Z^4+_Z^5-_Z^3))*n!

%F a(n)= n!*A052532(n). - _R. J. Mathar_, Nov 27 2011

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

%t With[{nn=20},CoefficientList[Series[(1-x)/(1-x-x^3-x^4+x^5),{x,0,nn}],x] Range[0,nn]!] (* _Harvey P. Dale_, Apr 27 2014 *)

%K easy,nonn

%O 0,4

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