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Keywords:
binomial coefficient; Catalan numbers, Super Catalan numbers, $q$-identity
binomial coefficient; Catalan numbers, Super Catalan numbers, $q$-identity
Summary:
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 $S(m,n)$.
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