OFFSET
0,3
COMMENTS
Conjectured to consist entirely of integers.
Compare to: C(x) = exp( Sum_{n>=1} C(x)^n*x^n/n ) where C(x) = g.f. of Catalan numbers (A000108).
EXAMPLE
G.f.: A(x) = 1 + x + 3*x^2 + 19*x^3 + 237*x^4 + 5741*x^5 + 270857*x^6 +...
A(x) = exp(A(2x)*x + A(4x)^2*x^2/2 + A(8x)^3*x^3/3 + A(16x)^4*x^4/4 +...).
PROG
(PARI) {a(n)=local(A=1+x); for(i=1, n, A=exp(sum(m=1, n, subst(A, x, 2^m*x +x*O(x^n))^m*x^m/m))); polcoeff(A, n)}
CROSSREFS
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Mar 06 2009
STATUS
approved