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%I
%S 1,1,1,6,27,168,1395,12744,136521,1672704,22659993,340472160,
%T 5605239123,100154133504,1933748430939,40097756280960,888588043228305,
%U 20962928129900544,524479633529596209,13871161113800394240
%N E.g.f. satisfies: A'(x) = 1 + x*A(x)^3 where A(0) = 1.
%H Vaclav Kotesovec, <a href="/A144013/b144013.txt">Table of n, a(n) for n = 0..286</a>
%F E.g.f. satisfies: A(x) = 1 + Integral [1 + x*A(x)^3] dx.
%F a(n) ~ n^n / (exp(n) * r^(n+1)), where r = 0.69974580613381637... - _Vaclav Kotesovec_, Feb 24 2014
%e E.g.f.: A(x) = 1 + x + x^2/2! + 6*x^3/3! + 27*x^4/4! + 168*x^5/5! +...
%e A(x)^3 = 1 + 3*x + 9*x^2/2! + 42*x^3/3! + 279*x^4/4! + 2124*x^5/5! +...
%e x*A(x)^3 = x + 6*x^2/2! + 27*x^3/3! + 168*x^4/4! + 1395*x^5/5! +...
%e A'(x) = 1 + x + 6*x^2/2! + 27*x^3/3! + 168*x^4/4! + 1395*x^5/5! +...
%o (PARI) {a(n)=local(A=1+x); for(i=0, n, A=1+intformal(1+x*(A+x*O(x^n))^3)); n!*polcoeff(A, n)}
%Y Cf. A144012, A144014.
%K nonn
%O 0,4
%A _Paul D. Hanna_, Sep 10 2008
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