A144008 - OEIS

%I #7 Jul 15 2014 03:25:10

%S 1,1,3,12,69,504,4455,46512,558873,7599744,115401915,1935368640,

%T 35529636285,708677828352,15261101987391,352891976935680,

%U 8721014464717425,229385791746109440,6398158947146344755

%N E.g.f. satisfies: A'(x) = (1 + x*A(x))^3 with A(0)=1.

%C Compare the definition of the e.g.f. A(x) to the trivial statement:

%C if F(x) = 1/(1-x) then F'(x) = (1 + x*F(x))^2.

%H Vaclav Kotesovec, <a href="/A144008/b144008.txt">Table of n, a(n) for n = 0..295</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+2)), where r = 0.628168728379601723852469... - _Vaclav Kotesovec_, Feb 24 2014

%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. A144009, A245247, A245248, A245249.

%K nonn

%O 0,3

%A _Paul D. Hanna_, Sep 10 2008