\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 Edward A. Bender, E. Rodney Canfield and L. Bruce Richmond}
%
%
\medskip
\noindent
%
%
{\bf Coefficients of Functional Compositions Often Grow Smoothly}
%
%
\vskip 5mm
\noindent
%
%
%
%
The coefficients of a power series $A(x)$ are smooth if $a_{n-1}/a_n$
approaches a limit.  If $A(x)=F(G(x))$ and $f_n^{1/n}$ approaches a
limit, then the coefficients of $A(x)$ are often smooth.  We use this
to show that the coefficients of the exponential generating function
for graphs embeddable on a given surface are smooth, settling a
problem of McDiarmid.



\bye

.