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A245249 E.g.f. satisfies: A'(x) = (1 + x*A(x))^7 with A(0)=1. 5

%I #5 Jul 15 2014 03:24:42

%S 1,1,7,56,609,8960,162015,3455760,85499505,2407507200,75954495015,

%T 2654662651200,101833013541105,4253509461922560,192174397814079135,

%U 9338303873329240320,485654062232697912225,26915598265961374986240,1583628181230906140008455

%N E.g.f. satisfies: A'(x) = (1 + x*A(x))^7 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="/A245249/b245249.txt">Table of n, a(n) for n = 0..265</a>

%F E.g.f. satisfies: A(x) = 1 + Integral (1 + x*A(x))^7 dx.

%F a(n) ~ c * d^n * n! / n^(5/6), where d = 3.4216107680..., c = 0.68714396...

%o (PARI) {a(n)=local(A=1+x); for(i=0, n, A=1+intformal((1+x*A+x*O(x^n))^7)); 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), A245248 (p=6).

%K nonn,easy

%O 0,3

%A _Vaclav Kotesovec_, Jul 15 2014

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