THE $k$-BINOMIAL AND CATALAN TRANSFORMS OF THE $k$-LEONARDO NUMBERS

Year 2025, Volume: 15 Issue: 11, 2652 - 2663, 03.11.2025

Kalika Prasad , Munesh Kumari , Hrishikesh Mahato

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.

Keywords

Leonardo numbers , $k$-binomial transform , Catalan transform , Generating function , Hankel transform

Thanks

The authors are thankful to the anonymous reviewers for their advice and fruitful corrections.

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