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

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

K. Prasad, M. Kumari, H. Mahato

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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.