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

%I #18 Jun 26 2022 10:47:26

%S 0,0,2,18,158,1530,16622,201978,2724878,40492890,657944942,

%T 11611834938,221291822798,4530383962650,99179581033262,

%U 2312402554523898,57211901491595918,1497211181084718810

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

%C Previous name was: A simple grammar.

%H INRIA Algorithms Project, <a href="http://ecs.inria.fr/services/structure?nbr=847">Encyclopedia of Combinatorial Structures 847</a>

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

%F From Mario Catalani (mario.catalani(AT)unito.it), Dec 22 2003: (Start)

%F a(n) = A069321(n) - A000670(n).

%F a(n) = 2*A091106(n)+2. (End)

%p 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 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 Cf. A000670, A069321, A091106.

%K easy,nonn

%O 0,3

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

%E Name changed by _Wesley Ivan Hurt_, Jun 26 2022