%I #15 Jan 29 2023 15:31:11

%S 1,2,8,54,480,5400,72720,1144080,20563200,415860480,9344160000,

%T 230958604800,6227499801600,181909958630400,5722470212659200,

%U 192874123233792000,6934147333521408000,264875092391669760000

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

%H INRIA Algorithms Project, <a href="http://ecs.inria.fr/services/structure?nbr=609">Encyclopedia of Combinatorial Structures 609</a>

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

%F Recurrence: {a(0)=1, a(1)=2, a(2)=8, (n^3+6*n^2+11*n+6)*a(n)+(-n^2-5*n-6)*a(n+1)+(-2*n-6)*a(n+2)+a(n+3)=0}

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

%F a(n) = n!*A052534(n). - _R. J. Mathar_, Nov 27 2011

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

%t With[{nn=20},CoefficientList[Series[(1-x^2)/(1-2x-x^2+x^3),{x,0,nn}],x] Range[ 0,nn]!] (* _Harvey P. Dale_, Jan 29 2023 *)

%K easy,nonn

%O 0,2

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