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%I #15 Sep 12 2023 20:30:31
%S 1,1,1,3,10,39,170,788,3885,20060,107989,603762,3496305,20943217,
%T 129663393,829488918,5483243950,37460570247,264551156875,
%U 1931501448369,14578396143512,113720726834349,916367532085433,7622370642112803,65390072935144713,577947703151643232
%N G.f. satisfies: A(x) = Sum_{n>=0} x^n * A(x)^(n^2) / (1 + x*A(x)^n)^n.
%C Note that if G(x) = Sum_{n>=0} x^n*G(x)^(n^2)/(1 + x*G(x)^n)^(n+1), then G(x) = 1.
%C Note that if F(x) = Sum_{n>=0} x^n*F(x)^n / (1 + x*F(x))^n, then F(x) = 1/(1-x).
%H Paul D. Hanna, <a href="/A221585/b221585.txt">Table of n, a(n) for n = 0..300</a>
%e G.f.: A(x) = 1 + x + x^2 + 3*x^3 + 10*x^4 + 39*x^5 + 170*x^6 + 788*x^7 +...
%e where
%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 + x^4*A(x)^16/(1 + x*A(x)^4)^4 + x^5*A(x)^25/(1 + x*A(x)^5)^5 +...
%o (PARI) {a(n)=local(A=1+x);for(i=1,n,A=sum(m=0, n, x^m*A^(m^2)/(1+x*subst(A,x,x+x*O(x^n))^m)^m));polcoeff(A, n)}
%o for(n=0, 30, print1(a(n), ", "))
%Y Cf. A301928, A221546, A221586.
%K nonn
%O 0,4
%A _Paul D. Hanna_, Jan 20 2013
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