A determinantal expression and a recursive relation of the Delannoy numbers

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.

Keywords

• delannoy number
• central delannoy number
• determinantal expression
• recursive relation
• primary 11b83
• secondary 05a15, 05a10, 11b75, 11c20, 60g50