|
%I #5 Jul 15 2014 03:23:40
%S 1,1,5,30,255,2880,39495,640800,12048225,257203200,6146830125,
%T 162636676800,4719436701375,149035892832000,5088353594517375,
%U 186769650799200000,7334368923555410625,306830158711872000000,13623286425863528263125,639832207565577018240000
%N E.g.f. satisfies: A'(x) = (1 + x*A(x))^5 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="/A245247/b245247.txt">Table of n, a(n) for n = 0..290</a>
%F E.g.f. satisfies: A(x) = 1 + Integral (1 + x*A(x))^5 dx.
%F a(n) ~ c * d^n * n! / n^(3/4), where d = 2.56982683907..., c = 0.803451595...
%o (PARI) {a(n)=local(A=1+x); for(i=0, n, A=1+intformal((1+x*A+x*O(x^n))^5)); 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), A245248 (p=6), A245249 (p=7).
%K nonn,easy
%O 0,3
%A _Vaclav Kotesovec_, Jul 15 2014
|
