Coefficients of Functional Compositions Often Grow Smoothly - Bender, Edward A.; Canfield, E. Rodney; Richmond, L. Bruce (The Electronic Journal of Combinatorics, 2008)
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.