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Counting Rooted Trees: The Universal Law t(n) ~ C ρ^{-n} n^{-3/2}

Jason P. Bell·Stanley N. Burris·Karen A. Yeats
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Abstract

Combinatorial classes T that are recursively defined using combinations of the standard multiset, sequence, directed cycle and cycle constructions, and their restrictions, have generating series 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 ρ^{-n} n^{-3/2} where ρis the radius of convergence of T.

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Jason P. Bell, Stanley N. Burris, Karen A. Yeats. 2006-08-09. Counting Rooted Trees: The Universal Law t(n) ~ C ρ^{-n} n^{-3/2}. https://arxiv.org/abs/math/0512432

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