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arXiv · 2505.09636

Three combinatorial sums involving central binomial coefficients

Kunle Adegoke·Robert Frontczak
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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.

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Kunle Adegoke, Robert Frontczak. 2025-05-04. Three combinatorial sums involving central binomial coefficients. https://arxiv.org/abs/2505.09636

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