Journal of Integer Sequences, Vol. 26 (2023), Article 23.4.4

On Some Binomial Coefficient Identities with Applications

Necdet Batır, Sezer Sorgun, and Sevda Atpınar
Department of Mathematics
Nevşehir Hacı Bektaş Veli University
50300 Nevşehir


In this paper, we present an alternative proof for a generalization of a binomial identity by Simons, initially proven by Munarini. Unlike previous proofs, our approach uses the Taylor theorem and the Wilf-Zeilberger algorithm. We also offer a new binomial sum identity and generalize a combinatorial identity by Alzer and Kouba. Additionally, we derive several harmonic number identities, including the proof for Hn and a formula involving the square of binomial coefficients and harmonic numbers.

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Received January 10 2023; revised versions received January 13 2023; January 16 2023; April 17 2023. Published in Journal of Integer Sequences, April 18 2023.

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