Journal of Integer Sequences, Vol. 22 (2019), Article 19.7.7

Two New Identities Involving the Catalan Numbers and Sign-Reversing Involutions

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


We give a combinatorial proof of a known sum concerning the product of a binomial coefficient with two central binomial coefficients. The method of description, involution, and exception is used. The same combinatorial argument also proves the "-1 shifted version" of this sum. As a consequence, two new binomial coefficient identities with the Catalan numbers are derived.

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Received May 5 2019; revised versions received May 13 2019; May 26 2019; November 9 2019. Published in Journal of Integer Sequences, November 11 2019.

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