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Hindawi, International Journal of Mathematics and Mathematical Sciences, (2021), p. 1-6, 2021

DOI: 10.1155/2021/9987314

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Catalan Transform of k -Balancing Sequences

Journal article published in 2021 by Asim Patra, Mohammed K. A. Kaabar ORCID
This paper is made freely available by the publisher.
This paper is made freely available by the publisher.

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Abstract

In this work, the Catalan transformation (CT) of k -balancing sequences, B k , n n ≥ 0 , is introduced. Furthermore, the obtained Catalan transformation C B k , n n ≥ 0 was shown as the product of lower triangular matrices called Catalan matrices and the matrix of k -balancing sequences, B k , n n ≥ 0 , which is an n × 1 matrix. Apart from that, the Hankel transform is applied further to calculate the determinant of the matrices formed from C B k , n n ≥ 0 .