Three combinatorial sums involving central binomial coefficients

Name: Three combinatorial sums involving central binomial coefficients
Keywords: Mathematics - Number Theory, 30B50, 33E20, FOS: Mathematics, Mathematics - Combinatorics, Number Theory (math.NT), Combinatorics (math.CO)

descriptionPublicationkeyboard_double_arrow_right Article , Preprint 01 Jan 2025Embargo end date: 01 Jan 2025Publisher:arXiv

Authors: Adegoke, Kunle; Frontczak, Robert;

doi: 10.48550/arxiv.2505.09636

arXiv: http://arxiv.org/abs/2505.09636

Three combinatorial sums involving central binomial coefficients

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Abstract

We study three classes of combinatorial sums involving central binomial coefficients and harmonic numbers, odd harmonic numbers, and even indexed harmonic numbers, respectively. In each case we use summation by parts to derive recursive expressions for these sums. In addition, we offer an alternative approach to express one class of sums and some related sums in closed form in terms of Stirling numbers and r-Stirling numbers of the second kind.

Keywords

Mathematics - Number Theory, 30B50, 33E20, FOS: Mathematics, Mathematics - Combinatorics, Number Theory (math.NT), Combinatorics (math.CO)

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