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{\bf Edward A. Bender, E. Rodney Canfield and L. Bruce Richmond}
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{\bf Coefficients of Functional Compositions Often Grow Smoothly}
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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