%I #6 Apr 28 2018 14:35:11
%S 1,15,291,20868,2501535,406641390,82021892979,19576367780568,
%T 5370958558206975,1661471768423203359,571522497313691705223,
%U 216322544080204799422227,89344723486622904627485286,39989870323587920736747152457,19285197574525200774860259575856,9970552400727667627167081347333058,5502200681071110455003310691040648913
%N G.f. A(x) satisfies: 1 = Sum_{n>=0} ( 3*(1+x)^n - A(x) )^n / 3^(n+1).
%H Paul D. Hanna, <a href="/A303653/b303653.txt">Table of n, a(n) for n = 0..50</a>
%F G.f.: 1 = Sum_{n>=0} 3^n * (1+x)^(n^2) / (3 + (1+x)^n * A(x))^(n+1).
%e G.f.: A(x) = 1 + 15*x + 291*x^2 + 20868*x^3 + 2501535*x^4 + 406641390*x^5 + 82021892979*x^6 + 19576367780568*x^7 + 5370958558206975*x^8 + ...
%e such that
%e 1 = 1/3 + (3*(1+x) - A(x))/3^2 + (3*(1+x)^2 - A(x))^2/3^3 + (3*(1+x)^3 - A(x))^3/3^4 + (3*(1+x)^4 - A(x))^4/3^5 + (3*(1+x)^5 - A(x))^5/3^6 + ...
%e Also,
%e 1 = 1/(3 + A(x)) + 3*(1+x)/(3 + (1+x)*A(x))^2 + 3^2*(1+x)^4/(3 + (1+x)^2*A(x))^3 + 3^3*(1+x)^9/(3 + (1+x)^3*A(x))^4 + 3^4*(1+x)^16/(3 + (1+x)^4*A(x))^5 + 3^5*(1+x)^25/(3 + (1+x)^5*A(x))^6 + ...
%Y Cf. A301436.
%K nonn
%O 0,2
%A _Paul D. Hanna_, Apr 28 2018