Journal of Integer Sequences, Vol. 24 (2021), Article 21.8.3

The Asymptotics of Factorials, Binomial Coefficients and Catalan Numbers


David A. Kessler
Department of Physics
Bar-Ilan University
Ramat Gan, 5290002
Israel

Jeremy Schiff
Department of Mathematics
Bar-Ilan University
Ramat Gan, 5290002
Israel

Abstract:

We present a variety of not-well-known asymptotic series for factorials, binomial coefficients and Catalan numbers, all having only even or odd powers. We discuss the significance of this property in terms of the asymptotic evenness or oddness of the underlying quantities.

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(Concerned with sequences A220002 A220422 A239739.)

Received April 11 2021; revised versions received August 9 2021; August 13 2021. Published in Journal of Integer Sequences, August 14 2021.

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