Hankel transform of linear combination of three consecutive Catalan numbers

Year 2025, Volume: 54 Issue: 4, 1470 - 1478, 29.08.2025

Radica Bojičić , M.d. Petković , Paul Barry

https://doi.org/10.15672/hujms.1564485

https://izlik.org/JA64HB79XK

Abstract

In this paper, we consider the Hankel determinants of the linear combination of three consecutive Catalan numbers, and then three consecutive shifted Catalan numbers. For their computing, we apply known methods based on the connections between continued fractions, orthogonal polynomials and moment-determinants. The properties of orthogonal polynomials enable us to evaluate the generating function of the corresponding sequence Hankel determinants in closed form.

Keywords

Catalan numbers , shifted Catalan numbers , Hankel transform , orthogonal polynomials

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