The k-binomial and Catalan transforms of the k-Leonardo numbers

Abstract

In this paper, we investigate the binomial transform and the Catalan transform of the k-Leonardo numbers and examine the new integer sequences. We apply the k-binomial, rising k-binomial, and falling k-binomial transforms to the k-Leonardo sequences. Further, we study the associated generating and exponential generating functions for these transforms. Finally, we implement the Hankel transform on the Catalan transforms of the k-Leonardo numbers to obtain the determinant of Hankel sub-matrices.