Some Double Sums Involving Ratios of Binomial Coefficients Arising From Urn Models
Mathematics and Statistics
Åbo Akademi University
James G. Wan
Engineering Systems and Design
Singapore University of Technology and Design
8 Somapah Road, 487372
School of Mathematical and Physical Sciences
The University of Newcastle
Callaghan NSW 2308
In this paper we discuss a class of double sums involving ratios of binomial coefficients. The sums are of the form
are functions of n
. Such sums appear in the analyses of the Mabinogion urn and the Ehrenfest urn in probability. Using hypergeometric functions, we are able to simplify these sums, and in some cases express them in terms of the harmonic numbers.
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(Concerned with sequences
Received September 25 2018; revised version received January 24 2019.
Published in Journal of Integer Sequences,
February 15 2019.
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