OFFSET
0,2
COMMENTS
From Vaclav Kotesovec, Oct 23 2020: (Start)
In general, for k>=1, if g.f. satisfies: A(x) = (1 + x*d/dx[x*A(x)] )^k, then a(n) ~ c(k) * k^n * n! * n^((k-1)/k), where c(k) is a constant (dependent only on k).
c(k) tends to A238223*exp(1) = 0.592451670452494179138706... if k tends to infinity.
(End)
LINKS
Vaclav Kotesovec, Table of n, a(n) for n = 0..330
FORMULA
G.f. satisfies: A(x) = (1 + x*d/dx[x*A(x)] )^8.
a(n) ~ c * 8^n * n! * n^(7/8), where c = 0.6523348263871879460325... - Vaclav Kotesovec, Oct 23 2020
PROG
(PARI) {a(n)=local(A=1+x*O(x^n)); for(i=1, n, A=(1+x*deriv(x*A))^8); polcoeff(A, n, x)}
CROSSREFS
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Nov 04 2005
STATUS
approved