OFFSET
0,3
LINKS
Vaclav Kotesovec, Table of n, a(n) for n = 0..400
FORMULA
G.f. satisfies: A(x) = 1 + x*A(x)^2*(2 - A(x)) + 2*x^2*A'(x)*A(x).
a(n) ~ c * n! * 2^n, where c = 0.343014753433948245763329120820010283... - Vaclav Kotesovec, Feb 22 2014
EXAMPLE
G.f.: A(x) = 1 + x + 3*x^2 + 16*x^3 + 123*x^4 + 1221*x^5 +...
A(x)^2 = 1 + 2*x + 7*x^2 + 38*x^3 + 287*x^4 + 2784*x^5 +...
log(1+x*A(x)^2) = x + 3*x^2/2 + 16*x^3/3 + 123*x^4/4 + 1221*x^5/5 +...
PROG
(PARI) {a(n)=local(A=1+x); for(i=1, n, A=1+x*deriv(log(1+x*Ser(A)^2)+x*O(x^n))); polcoeff(A, n)}
CROSSREFS
KEYWORD
nonn
AUTHOR
Paul D. Hanna, May 16 2009
STATUS
approved