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Abstract We show that, for all positive integers , , and any non-negative integers j and r with , the expression is a Laurent polynomial in q with integer coefficients,… Click to show full abstract
Abstract We show that, for all positive integers , , and any non-negative integers j and r with , the expression is a Laurent polynomial in q with integer coefficients, where and . This gives a q-analogue of a divisibility result on the Catalan triangle obtained by the first author and Zeng, and also confirms a conjecture of the first author and Zeng. We further propose several related conjectures.
Keywords:
coefficients powers;
sums involving;
factors sums;
involving binomial;
binomial coefficients;
powers integers
Journal Title: Journal of Difference Equations and Applications
Year Published: 2017
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Journal Title: Journal of Difference Equations and Applications
Year Published: 2017
Link to full text (if available)
Share on Social Media: Sign Up to like & get
recommendations!