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G.f.: A(x) = exp( Sum_{n>=1} A(3^n*x)^n * x^n/n ).
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%I #2 Mar 30 2012 18:37:17

%S 1,1,4,49,1768,187474,58888462,55210937881,155033790773008,

%T 1305338879106660550,32966118096763299572020,

%U 2497521410388697783376754490,567627952695201383291867693446222

%N G.f.: A(x) = exp( Sum_{n>=1} A(3^n*x)^n * x^n/n ).

%C Compare to: C(x) = exp( Sum_{n>=1} C(x)^n*x^n/n ) where C(x) = g.f. of Catalan numbers (A000108).

%e G.f.: A(x) = 1 + x + 4*x^2 + 49*x^3 + 1768*x^4 + 187474*x^5 +...

%e log(A(x)) = x + 7*x^2/2 + 136*x^3/3 + 6859*x^4/4 + 927856*x^5/5 +...

%e log(A(x)) = A(3x)*x + A(9x)^2*x^2/2 + A(27x)^3*x^3/3 + A(81x)^4*x^4/4 +...

%o (PARI) {a(n)=local(A=1+x);for(n=2,n, A=exp(sum(k=1,n,subst(A,x,3^k*x+x*O(x^n))^k*x^k/k)));polcoeff(A,n)}

%Y Cf. A157675.

%K nonn

%O 0,3

%A _Paul D. Hanna_, May 02 2009