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A176719 G.f. satisfies: A(x) = 1 + Sum_{n>=1} 2*x^n * A(x)^(n^2).

%I A176719 #6 Jun 16 2014 19:20:19
%S A176719 1,2,6,30,194,1442,11782,103102,951554,9173186,91780614,948985822,
%T A176719 10110931650,110794764642,1247186300934,14412811665278,
%U A176719 170949340705794,2081185257723778,26012832364535814,333929563132811678,4404347475363755714,59705917899701420834,832080588205468939782
%N A176719 G.f. satisfies: A(x) = 1 + Sum_{n>=1} 2*x^n * A(x)^(n^2).
%H A176719 Paul D. Hanna, <a href="/A176719/b176719.txt">Table of n, a(n) for n = 0..100</a>
%F A176719 Contribution from _Paul D. Hanna_, May 11 2010: (Start)
%F A176719 Given g.f. A(x), then Q = A(-x^2) satisfies:
%F A176719 Q = (1-x)*Sum_{n>=0} x^n*Product_{k=1..n} (1 - x*Q^k)/(1 + x*Q^k)
%F A176719 due to a q-series expansion for the Jacobi theta_4 function. (End)
%e A176719 G.f.: A(x) = 1 + 2*x + 6*x^2 + 30*x^3 + 194*x^4 + 1442*x^5 +...
%e A176719 A(x) = 1 + 2*x*A(x) + 2*x^2*A(x)^4 + 2*x^3*A(x)^9 + 2*x^4*A(x)^16 + ...
%e A176719 Contribution from _Paul D. Hanna_, May 11 2010: (Start)
%e A176719 Given g.f. A(x), then Q = A(-x^2) satisfies the q-series:
%e A176719 Q/(1-x) = 1 + x*(xQ;Q)_1/(-xQ;Q)_1 + x^2*(xQ;Q)_2/(-xQ;Q)_2 +...
%e A176719 where the q-Pochhammer symbol (x;q)_n = Product_{k=0..n-1} (1-x*q^k). (End)
%o A176719 (PARI) {a(n)=local(A=1+x);for(i=1,n,A=1+sum(m=1,n,2*x^m*(A+x*O(x^n))^(m^2)));polcoeff(A,n)}
%o A176719 for(n=0,25,print1(a(n),", "))
%Y A176719 Cf. A107595, A176720.
%K A176719 nonn
%O A176719 0,2
%A A176719 _Paul D. Hanna_, Apr 25 2010
%E A176719 Edited by _Paul D. Hanna_, Apr 27 2010