Proofs of two conjectures on Catalan triangle numbers
arXiv:1806.02685
Abstract
We prove two conjectures on sums of products of Catalan triangle numbers, which were originally conjectured by Miana, Ohtsuka, and Romero [Discrete Math. 340 (2017), 2388--2397]. The first one is proved by using Zeilberger's algorithm, and the second one is proved by establishing its -analogue.
15 pages, to appear in J. Difference Equ. Appl