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G.f. satisfies: A(x) = Sum_{n>=0} x^(n^2)*A(x)^(n^3).
1

%I #5 Mar 30 2012 18:37:26

%S 1,1,1,1,2,10,46,166,504,1425,4256,14594,55783,220903,873199,3436817,

%T 13569556,53929244,215352055,861477251,3446980935,13792641374,

%U 55203566064,221112089602,887538377345,3580304912835,14573568107348

%N G.f. satisfies: A(x) = Sum_{n>=0} x^(n^2)*A(x)^(n^3).

%e G.f.: A(x) = 1 + x + x^2 + x^3 + 2*x^4 + 10*x^5 + 46*x^6 + 166*x^7 +...

%e where the g.f. satisfies:

%e A(x) = 1 + x*A(x) + x^4*A(x)^8 + x^9*A(x)^27 + x^16*A(x)^64 + x^25*A(x)^125 + x^36*A(x)^216 +...+ x^(n^2)*A(x)^(n^3) +...

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

%Y Cf. A157134, A157136, A191814.

%K nonn

%O 0,5

%A _Paul D. Hanna_, Jun 17 2011