OFFSET
0,3
LINKS
Vaclav Kotesovec, Table of n, a(n) for n = 0..300
FORMULA
G.f. satisfies: A(x) = 1 + x*(2 - A(x))*A(x)^3 + 3*x^2*A'(x)*A(x)^2.
a(n) ~ c * 3^n * n! * n^(1/3), where c = 0.242604467523310747298... - Vaclav Kotesovec, Aug 24 2017
EXAMPLE
G.f.: A(x) = 1 + x + 5*x^2 + 46*x^3 + 597*x^4 + 9791*x^5 +...
A(x)^3 = 1 + 3*x + 18*x^2 + 169*x^3 + 2157*x^4 + 34548*x^5 +...
log(1+x*A(x)^3) = x + 5*x^2/2 + 46*x^3/3 + 597*x^4/4 + 9791*x^5/5 +...
PROG
(PARI) {a(n)=local(A=1+x); for(i=1, n, A=1+x*deriv(log(1+x*Ser(A)^3)+x*O(x^n))); polcoeff(A, n)}
CROSSREFS
KEYWORD
nonn
AUTHOR
Paul D. Hanna, May 16 2009
STATUS
approved