A052623 - OEIS

%I #15 Jun 03 2022 18:35:20

%S 0,1,2,18,192,2520,39600,725760,15200640,358162560,9376819200,

%T 270037152000,8483597337600,288734500454400,10582834303641600,

%U 415593298568448000,17408598098411520000,774797125808369664000

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

%H INRIA Algorithms Project, <a href="http://ecs.inria.fr/services/structure?nbr=569">Encyclopedia of Combinatorial Structures 569</a>

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

%F Recurrence: {a(1)=1, a(0)=0, a(2)=2, (n^2+3*n+2)*a(n)+(-6-3*n)*a(n+1)+a(n+2)=0, a(3)=18}

%F Sum(-1/5*(-3+7*_alpha)*_alpha^(-1-n), _alpha=RootOf(_Z^2-3*_Z+1))*n!

%F a(n)=n!*A088305(n-1). - _R. J. Mathar_, Jun 03 2022

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

%t With[{nn=20},CoefficientList[Series[x (1-x)^2/(1-3x+x^2),{x,0,nn}],x] Range[ 0,nn]!] (* _Harvey P. Dale_, May 30 2021 *)

%K easy,nonn

%O 0,3

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