Journal of Integer Sequences, Vol. 23 (2020), Article 20.1.6

On Certain Sums Divisible by the Central Binomial Coefficient

Jovan Mikić
J.U. SŠC "Jovan Cvijić"
74480 Modriča
Republic of Srpska


We prove that some sums, which arise as generalizations of known binomial coefficient identities, are divisible by the central binomial coefficient. A new method is used. In particular, we show that an alternating sum concerning the product of a power of a binomial coefficient with two Catalan numbers is always divisible by the central binomial coefficient.

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Received May 21 2019; revised version received June 5 2019; November 16 2019; November 17 2019. Published in Journal of Integer Sequences, December 30 2019.

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