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G.f. satisfies: A(x) = Sum_{n>=0} x^n*A(x)^(n^2)/(1 - x*A(x)^n)^n.
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%I #4 Mar 30 2012 18:37:27

%S 1,1,3,13,70,431,2904,20884,157881,1242470,10111281,84700640,

%T 727952319,6403738619,57563742289,528125896942,4941448428666,

%U 47128664659641,458055597979709,4536505547203889,45785021320327540,470972703324515813

%N G.f. satisfies: A(x) = Sum_{n>=0} x^n*A(x)^(n^2)/(1 - x*A(x)^n)^n.

%e G.f.: A(x) = 1 + x + 3*x^2 + 13*x^3 + 70*x^4 + 431*x^5 + 2904*x^6 +...

%e which satisfies:

%e A(x) = 1 + x*A(x)/(1-x*A(x)) + x^2*A(x)^4/(1-x*A(x)^2)^2 + x^3*A(x)^9/(1-x*A(x)^3)^3 +...

%o (PARI) {a(n)=local(A=1+x); for(i=1, n, A=1+sum(m=1, n, x^m*A^(m^2)/(1-x*A^m+x*O(x^n))^m)); polcoeff(A, n)}

%K nonn

%O 0,3

%A _Paul D. Hanna_, Jun 25 2011