OFFSET
0,3
COMMENTS
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.
LINKS
Vaclav Kotesovec, Table of n, a(n) for n = 0..300
FORMULA
E.g.f. satisfies: A(x) = 1 + Integral (1 + x*A(x))^6 dx.
a(n) ~ c * d^n * n! / n^(4/5), where d = 3.00663532009..., c = 0.73726997...
PROG
(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)}
for(n=0, 20, print1(a(n), ", "))
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Vaclav Kotesovec, Jul 15 2014
STATUS
approved