  For the solutions $\Phi(z)$ of functional equations
$\Phi(z)=P(z)+\Phi(Q(z))$, we derive a complete asymptotic of power series
coefficients. As an application, we improve significantly an asymptotic of the
number of $2,3$-trees with $n$ leaves given in Adv. Math. 44:180-205, 1982 by
Andrew M. Odlyzko. The methods we consider can be applied to more general
functional equations too.
