OFFSET
0,3
COMMENTS
Compare g.f. with: G(x) = exp(Sum_{n>=1} (2 - G(x))^n * x^n/n) = 1 + x*C(-x^2) where C(x) is the Catalan function (A000108).
EXAMPLE
G.f.: A(x) = 1 + x + 4*x^2 + 111*x^3 + 12600*x^4 + 5722258*x^5 +...
where
log(A(x)) = (2 - A(x))*x + (2^2 - A(x))^2*x^2/2 + (2^3 - A(x))^3*x^3/3 + (2^4 - A(x))^4*x^4/4 +...
PROG
(PARI) {a(n)=local(A=1+x); for(i=1, n, A=exp(sum(m=1, n, (2^m-A+x*O(x^n))^m*x^m/m))); polcoeff(A, n)}
CROSSREFS
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Dec 20 2011
STATUS
approved