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%I #6 Aug 24 2017 09:00:22
%S 1,1,3,24,273,3996,70785,1465506,34662222,921511944,27201024639,
%T 882828325530,31253560065684,1198758613494852,49530067909218819,
%U 2193498057583259784,103664556373964098860,5207896547115772335552,277161367378578537506868
%N G.f. A(x) satisfies: A(x) = 1+x + x^2*[d/dx A(x)^3].
%H Vaclav Kotesovec, <a href="/A218223/b218223.txt">Table of n, a(n) for n = 0..320</a>
%F G.f. A(x) satisfies: A(x) = 1+x + 3*x^2*A(x)^2*A'(x).
%F a(n) ~ c * 3^n * n! / n^(1/3), where c = 0.3133426736012301024021... - _Vaclav Kotesovec_, Aug 24 2017
%e G.f.: A(x) = 1 + x + 3*x^2 + 24*x^3 + 273*x^4 + 3996*x^5 + 70785*x^6 +...
%e Related series:
%e A(x)^3 = 1 + 3*x + 12*x^2 + 91*x^3 + 999*x^4 + 14157*x^5 + 244251*x^6 +...
%e d/dx A(x)^3 = 3 + 24*x + 273*x^2 + 3996*x^3 + 70785*x^4 + 1465506*x^5 +...
%o (PARI) {a(n)=local(A=1+x); for(i=1, n, A=1+x+x^2*deriv(A^3+x*O(x^n))); polcoeff(A, n)}
%o for(n=0, 30, print1(a(n), ", "))
%Y Cf. A185183, A218224.
%K nonn
%O 0,3
%A _Paul D. Hanna_, Oct 23 2012
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