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%I #4 Mar 30 2012 18:36:46
%S 1,1,3,14,80,514,3567,26153,199900,1579107,12816020,106421359,
%T 901430144,7771535382,68085001080,605420138920,5459655601753,
%U 49904765136264,462228258349278,4337787743946224,41249375376404380,397572319756235577
%N G.f. satisfies: A(x) = Sum_{n>=0} x^n * A(x)^(n^2+n).
%F G.f. A(x)^2 = (1/x)*series-reversion(x/G107594(x)^2) and thus A(x) = G107594(x*A(x)^2) where G107594(x) is the g.f. of A107594. G.f. A(x) = (1/x)*series-reversion(x/G107595(x)) and thus A(x) = G107595(x*A(x)) where G107595(x) is the g.f. of A107595.
%F Contribution from _Paul D. Hanna_, Apr 25 2010: (Start)
%F Let A = g.f. A(x), then A satisfies the continued fraction:
%F A = 1/(1- A^2*x/(1- (A^4-A^2)*x/(1- A^6*x/(1- (A^8-A^4)*x/(1- A^10*x/(1- (A^12-A^6)*x/(1- A^14*x/(1- (A^16-A^8)*x/(1- A^18*x)))))))))
%F due to an identity of a partial elliptic theta function.
%F (End)
%e A = 1 + x*A^2 + x^2*A^6 + x^3*A^12 + x^4*A^20 + x^5*A^30 ...
%e = 1 + (x + 2*x^2 + 7*x^3 + 34*x^4 + 197*x^5 + 1272*x^6 +...)
%e + (x^2 + 6*x^3 + 33*x^4 + 194*x^5 + 1230*x^6 +...)
%e + (x^3 + 12*x^4 + 102*x^5 + 784*x^6 +...)
%e + (x^4 + 20*x^5 + 250*x^6 +...) +...
%e = 1 + x + 3*x^2 + 14*x^3 + 80*x^4 + 514*x^5 + 3567*x^6 +...
%o (PARI) {a(n)=local(A=1+x+x*O(x^n)); for(k=1,n,A=1+sum(j=1,n,x^j*A^(j^2+j)+x*O(x^n)));polcoeff(A,n)}
%Y Cf. A107592, A107594, A107595.
%K eigen,nonn
%O 0,3
%A _Paul D. Hanna_, May 17 2005
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