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A simple grammar.
4

%I #16 Jul 14 2024 15:29:34

%S 1,1,4,19,107,647,4167,27847,191747,1349743,9671316,70297105,

%T 517079157,3841701488,28787546360,217317367487,1651144126659,

%U 12616570941114,96891439504019,747452640586114,5789461514134881

%N A simple grammar.

%H INRIA Algorithms Project, <a href="http://ecs.inria.fr/services/structure?nbr=707">Encyclopedia of Combinatorial Structures 707</a>

%F G.f.: A(x) = exp(A(x)^3*x + A(x^2)^3*x^2/2 + A(x^3)^3*x^3/3 +...), A(0)=1; also, A(x)^3 = Sum_{n>=0} A006964(n+1)*x^n. - _Paul D. Hanna_, Jul 13 2006

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

%o (PARI) {a(n)=local(A=1+x+x*O(x^n));if(n==0,1,for(i=1,n, A=exp(sum(k=1,n,subst(x*A^3,x,x^k+x*O(x^n))/k)));polcoeff(A,n,x))} \\ _Paul D. Hanna_, Jul 13 2006

%Y Cf. A006964.

%K easy,nonn

%O 0,3

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