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A052876 Expansion of e.g.f. (exp(x)-1)^2/(-2+exp(x))^2.

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%I A052876 #18 Jun 26 2022 10:47:26
%S A052876 0,0,2,18,158,1530,16622,201978,2724878,40492890,657944942,
%T A052876 11611834938,221291822798,4530383962650,99179581033262,
%U A052876 2312402554523898,57211901491595918,1497211181084718810
%N A052876 Expansion of e.g.f. (exp(x)-1)^2/(-2+exp(x))^2.
%C A052876 Previous name was: A simple grammar.
%H A052876 INRIA Algorithms Project, <a href="http://ecs.inria.fr/services/structure?nbr=847">Encyclopedia of Combinatorial Structures 847</a>
%F A052876 E.g.f.: (exp(x)-1)^2/(-2+exp(x))^2.
%F A052876 From Mario Catalani (mario.catalani(AT)unito.it), Dec 22 2003: (Start)
%F A052876 a(n) = A069321(n) - A000670(n).
%F A052876 a(n) = 2*A091106(n)+2. (End)
%p A052876 spec := [S,{B=Set(Z,1 <= card),C=Sequence(B,1 <= card),S=Prod(C,C)},labeled]: seq(combstruct[count](spec,size=n), n=0..20);
%t A052876 With[{nn=20},CoefficientList[Series[((Exp[x]-1)^2/(Exp[x]-2)^2),{x,0,nn}],x] Range[0,nn]!] (* _Harvey P. Dale_, Jul 19 2018 *)
%Y A052876 Cf. A000670, A069321, A091106.
%K A052876 easy,nonn
%O A052876 0,3
%A A052876 encyclopedia(AT)pommard.inria.fr, Jan 25 2000
%E A052876 Name changed by _Wesley Ivan Hurt_, Jun 26 2022