Some aspects of Neyman triangles and Delannoy arrays

Abstract

This note considers some number theoretic properties of the orthonormal Neyman polynomials which are related to Delannoy numbers and certain complex Delannoy numbers.

New Narayana Triangle

“…which can also be expressed as which has echoes of the Catalan result Many of the pertinent number theory relations and connections have been elaborated by Carlitz and Riordan [11] and Deveci, Sloane, and Dişkaya [12][13][14]. There are many links to the Online Encyclopedia of Integer Sequences [13] with its rich links to the literature, for example, (Triangular numbers are referenced in the On-Line Encyclopedia of Integer Sequences.…”