Catalan Transform of k-Balancing Sequences

Abstract

In this work, the Catalan transformation (CT) of k-balancing sequences, Bk,nn≥0, is introduced. Furthermore, the obtained Catalan transformation CBk,nn≥0 was shown as the product of lower triangular matrices called Catalan matrices and the matrix of k-balancing sequences, Bk,nn≥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 CBk,nn≥0.