Asymptotics for a certain group of exponential generating functions
Vaclav Kotesovec
TL;DR
This paper derives asymptotic formulas for a class of exponential generating functions, including those related to several OEIS sequences, expanding understanding of their growth behavior.
Contribution
It introduces a general asymptotic analysis for exponential generating functions of the form exp(m*exp(b*x)+r*exp(d*x)+s), covering multiple OEIS sequences.
Findings
Derived asymptotic formulas for the sequences A143405, A355291, A002872, A002874.
Provided a unified approach to analyze exponential generating functions with multiple exponential terms.
Enhanced understanding of the growth rates of related combinatorial sequences.
Abstract
The exponential generating function for the sequence A143405 in the OEIS is exp(exp(x)*(exp(x) - 1)). This paper analyzes the more general generating function exp(m*exp(b*x) + r*exp(d*x) + s) and provides asymptotics for the sequences A143405, A355291, A002872, A002874 and others in the OEIS.
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Taxonomy
TopicsAlgorithms and Data Compression