%I #18 Feb 15 2020 13:06:08
%S 0,1,2,18,216,3720,81360,2172240,68423040,2484639360,102190636800,
%T 4695453100800,238382331264000,13251891094041600,800600878273996800,
%U 52229642780899584000,3659347096696811520000,274040260725697449984000
%N E.g.f. (1-sqrt(1-4*x-4*x^2))/ (2*(1+x)).
%H INRIA Algorithms Project, <a href="http://ecs.inria.fr/services/structure?nbr=682">Encyclopedia of Combinatorial Structures 682</a>
%F D-finite with recurrence: {a(1)=1, a(0)=0, a(2)=2, (-4*n^3-12*n^2-8*n)*a(n) +(-22*n-12-8*n^2)*a(n+1) +(-3*n-3)*a(n+2) +a(n+3) =0.
%F a(n) = n!*A052709(n). - _R. J. Mathar_, Oct 18 2013
%p spec := [S,{B=Prod(Z,C),S=Union(B,Z,C),C=Prod(S,S)},labeled]: seq(combstruct[count](spec,size=n), n=0..20);
%t With[{nn=20},CoefficientList[Series[(1-Sqrt[1-4x-4x^2])/(2(1+x)),{x,0,nn}],x] Range[0,nn]!] (* _Harvey P. Dale_, Feb 15 2020 *)
%K easy,nonn
%O 0,3
%A encyclopedia(AT)pommard.inria.fr, Jan 25 2000