<abstract xmlns="http://www.w3.org/1999/xhtml">

<p>In the paper, by a general and fundamental, but non-extensively circulated, formula for derivatives of a ratio of two differentiable functions and by a recursive relation of the Hessenberg determinant, the author finds a new determinantal expression and a new recursive relation of the Delannoy numbers. Consequently, the author derives a recursive relation for computing central Delannoy numbers in terms of related Delannoy numbers.</p>
</abstract>

In the paper, by a general and fundamental, but non-extensively circulated, formula for derivatives of a ratio of two differentiable functions and by a recursive relation of the Hessenberg determinant, the author finds a new determinantal expression and a new recursive relation of the Delannoy numbers. Consequently, the author derives a recursive relation for computing central Delannoy numbers in terms of related Delannoy numbers.

A determinantal expression and a recursive relation of the Delannoy numbers

Acta Universitatis Sapientiae, Mathematica

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

{"article-title":"A determinantal expression and a recursive relation of the Delannoy numbers"}

In the paper, by a general and fundamental, but non-extensively circulated, formula for derivatives of a ratio of two differentiable functions and by a...

A determinantal expression and a recursive relation of the Delannoy numbers

Published Online: Dec 30, 2021

Page range: 442 - 449

DOI: https://doi.org/10.2478/ausm-2021-0027

Keywords
Delannoy number, central Delannoy number, determinantal expression, recursive relation

© 2021 Feng Qi, published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

A determinantal expression and a recursive relation of the Delannoy numbers

Published Online: Dec 30, 2021

Page range: 442 - 449

DOI: https://doi.org/10.2478/ausm-2021-0027

KeywordsDelannoy number, central Delannoy number, determinantal expression, recursive relation

© 2021 Feng Qi, published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Keywords
Delannoy number, central Delannoy number, determinantal expression, recursive relation