We can know the growth rate of coefficients from singularities of generating functions, but if a generating function which has no singularity at all, for example, the exponential function. What information can we get about its coefficients?
2026-03-25 01:40:14.1774402814
Generating function which has no singularity
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Check out Flajolet and Sedgewick's "Analytic Combinatorics" (PDF available for free), it contains a very thorough discussion of such matters. Somewhat more approachable is Sedgewick and Flajolet's "Introduction to the analysis of algorithms".