Proofs of two conjectures on Catalan triangle numbers

2018/06/06 by Guo, Victor J. W., Lian, Xiuguo
#05A10 #05A30 #11B65 #Combinatorics (math.CO) #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/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 q-analogue.

Related

• Revitalized automatic proofs: demonstrations
• Sums of powers of Catalan triangle numbers
• Fuss-Catalan Triangles
• Catalan triangle numbers and binomial coefficients
• Four transformations on the Catalan triangle