OFFSET
0,3
COMMENTS
Compare to: M(x) = exp( Sum_{n>=1} (1 + x*M(x))^n * x^n/n ) where M(x) is the g.f. of the Motzkin numbers (A001006).
EXAMPLE
G.f.: A(x) = 1 + x + 3*x^2 + 9*x^3 + 37*x^4 + 183*x^5 + 1175*x^6 +...
log(A(x)) = x + 5*x^2/2 + 19*x^3/3 + 105*x^4/4 + 671*x^5/5 + 5525*x^6/6 +...
log(A(x)) = (1+2x*A(x))*x + (1+4x*A(x))^2*x^2/2 + (1+8x*A(x))^3*x^3/3 +...
PROG
(PARI) {a(n)=local(A=1+x); for(i=1, n, A=exp(sum(m=1, n, (1+2^m*x*A)^m*x^m/m+x*O(x^n)))); polcoeff(A, n)}
CROSSREFS
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Mar 11 2009
STATUS
approved