%I #16 Feb 13 2019 00:42:43
%S 0,0,2,12,168,3120,75600,2237760,78382080,3169393920,145297152000,
%T 7446479040000,421880659200000,26181558769766400,1766275594501017600,
%U 128700516232544256000,10073126652104355840000
%N A simple context-free grammar in a labeled universe.
%H INRIA Algorithms Project, <a href="http://ecs.inria.fr/services/structure?nbr=685">Encyclopedia of Combinatorial Structures 685</a>
%F E.g.f.: RootOf(-_Z+_Z^2+_Z^3+x)^2
%F Recurrence: {a(1)=0, a(2)=2, a(3)=12, (21*n-27*n^3-6)*a(n) +(-49*n^2-6-65*n)*a(n+1) +(-33-17*n)*a(n+2) +5*a(n+3) =0.
%F a(n) = n!*A052706(n). - _R. J. Mathar_, Oct 18 2013
%p spec := [S,{B=Prod(S,C),S=Prod(C,C),C=Union(B,S,Z)},labeled]: seq(combstruct[count](spec,size=n), n=0..20);
%p seq(2*add((n+k-1)!/(n-k-2)!/(2*k+2-n)!, k= ceil(n/2)-1..n-2),n=0..20); # _Mark van Hoeij_, May 12 2013
%K easy,nonn
%O 0,3
%A encyclopedia(AT)pommard.inria.fr, Jan 25 2000