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

Abstract:

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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