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%I #11 Mar 30 2012 18:37:27
%S 1,1,3,12,59,328,1987,12819,86840,611993,4458355,33425634,257101218,
%T 2024379762,16292282944,133886553125,1122781620139,9605824882455,
%U 83838618087996,746620718694421,6786473727400695,62988617523112588,597257517555481856
%N G.f. satisfies: A(x) = Product_{n>=1} 1/(1 - x^n*A(x)^(n^2)).
%F G.f. satisfies: A(x) = exp( Sum_{n>=1} (x^n/n)*Sum_{d|n} d*A(x)^(n*d) ).
%e G.f.: A(x) = 1 + x + 3*x^2 + 12*x^3 + 59*x^4 + 328*x^5 + 1987*x^6 +...
%e The g.f. A = A(x) satisfies the product:
%e A = 1/((1 - x*A)*(1 - x^2*A^4)*(1 - x^3*A^9)*(1 - x^4*A^16)*...)
%e as well as the logarithmic series:
%e log(A) = x*A + x^2*(A^2 + 2*A^4)/2 + x^3*(A^3 + 3*A^9)/3 + x^4*(A^4 + 2*A^8 + 4*A^16)/4 + x^5*(A^5 + 5*A^25)/5 + x^6*(A^6 + 2*A^12 + 3*A^18 + 6*A^36)/6 +...
%o (PARI) {a(n)=local(A=1+x);for(i=1,n,A=1/prod(k=1, n, 1-x^k*A^(k^2)+x*O(x^n)));polcoeff(A, n)}
%o (PARI) {a(n)=local(A=1+x);for(i=1,n,A=exp(sum(m=1,n,(x^m/m)*sumdiv(m,d,d*A^(m*d))+x*O(x^n))));polcoeff(A,n)}
%Y Cf. A192783, A192784.
%K nonn
%O 0,3
%A _Paul D. Hanna_, Jul 09 2011
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