Two New Identities Involving the Catalan Numbers and Sign-Reversing Involutions
J.U. SŠC "Jovan Cvijić"
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.
Full version: pdf,
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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