%I #5 Jul 15 2014 03:24:21
%S 1,1,6,42,408,5328,84960,1600128,34957440,868247424,24152048640,
%T 744116855040,25155056424960,925729237969920,36842642690181120,
%U 1576774342552872960,72212210263605657600,3523820406525504552960,182532196288859620147200,10003033225361632653803520
%N E.g.f. satisfies: A'(x) = (1 + x*A(x))^6 with A(0)=1.
%C In general, if e.g.f satisfies A'(x) = (1+x*A(x))^p, then a(n) ~ c(p) * d(p)^n * n! / n^(1-1/(p-1)), where c(p) and d(p) are constants independent on n.
%H Vaclav Kotesovec, <a href="/A245248/b245248.txt">Table of n, a(n) for n = 0..300</a>
%F E.g.f. satisfies: A(x) = 1 + Integral (1 + x*A(x))^6 dx.
%F a(n) ~ c * d^n * n! / n^(4/5), where d = 3.00663532009..., c = 0.73726997...
%o (PARI) {a(n)=local(A=1+x); for(i=0, n, A=1+intformal((1+x*A+x*O(x^n))^6)); n!*polcoeff(A, n)}
%o for(n=0, 20, print1(a(n), ", "))
%Y Cf. A006882(n-1) (p=1), A000142 (p=2), A144008 (p=3), A144009 (p=4), A245247 (p=5), A245249 (p=7).
%K nonn,easy
%O 0,3
%A _Vaclav Kotesovec_, Jul 15 2014