\magnification=1200
\hsize=4in
\overfullrule=0pt
\input amssym
%\def\frac#1 #2 {{#1\over #2}}
\def\emph#1{{\it #1}}
\def\em{\it}
\nopagenumbers
\noindent
%
%
{\bf Jason P. Bell, Stanley N. Burris and Karen A. Yeats }
%
%
\medskip
\noindent
%
%
{\bf Counting Rooted Trees: The Universal Law $t(n)\,\sim\,C \rho^{-n} n^{-3/2}$}
%
%
\vskip 5mm
\noindent
%
%
%
%
Combinatorial classes ${\cal T}$ that are recursively defined using
combinations of the standard \emph{multiset}, \emph{sequence},
\emph{directed cycle} and \emph{cycle} constructions, and their
restrictions, have generating series ${\bf T}(z)$ with a positive radius
of convergence; for most of these a simple test can be used to quickly
show that the form of the asymptotics is the same as that for the
class of rooted trees: $C \rho^{-n} n^{-3/2}$, where $\rho$ is the
radius of convergence of ${\bf T}$.
\bye