A052607 - OEIS

%I #16 Apr 18 2017 07:03:55

%S 1,0,2,0,24,120,720,10080,80640,1088640,14515200,199584000,3353011200,

%T 56043187200,1046139494400,20922789888000,439378587648000,

%U 9959247986688000,236887827111936000,5960609920032768000

%N E.g.f. (1-x^3)/(1-x^2-x^3).

%H INRIA Algorithms Project, <a href="http://ecs.inria.fr/services/structure?nbr=552">Encyclopedia of Combinatorial Structures 552</a>

%F E.g.f.: (-1+x^3)/(-1+x^2+x^3)

%F Recurrence: {a(1)=0, a(0)=1, a(3)=0, a(2)=2, (-11*n-6-n^3-6*n^2)*a(n) +(-n^2-5*n-6)*a(n+1) +a(n+3)=0}

%F Sum(-1/23*(6*_alpha^2+2*_alpha-9)*_alpha^(-1-n), _alpha=RootOf(_Z^3+_Z^2-1))*n!

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

%t With[{nn=20},CoefficientList[Series[(1-x^3)/(1-x^2-x^3),{x,0,nn}],x] Range[0,nn]!] (* _Harvey P. Dale_, Jan 04 2012 *)

%K easy,nonn

%O 0,3

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