Mathematica Bohemica, first online, pp. 1-10


On some $q$-generalization of Super Catalan numbers

Serpil Halıcı, Zehra Betül Gür

Received December 17, 2024.   Published online August 14, 2025.

Abstract:  The aim of this paper is to generalize the Super Catalan numbers $S(m,n)$ and some properties of them by virtue of $q$-Calculus. For this purpose, we focus on formulating several weighted sums and different representations of the Super Catalan number sequence. Moreover, we derive some $q$-identities involving the $q$-Super Catalan numbers as a generalization of the results obtained for the numbers $S(m,n)$.
Keywords:  binomial coefficient; Catalan numbers, Super Catalan numbers, $q$-identity
Classification MSC:  11B65, 05A10, 11B83

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Affiliations:   Serpil Halıcı, Zehra Betül Gür (corresponding author), Department of Mathematics, Pamukkale University, 20070 Denizli, Turkey, e-mail: shalici@pau.edu.tr, gurbetul35@gmail.com


 
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