Tuenter polynomials and a Catalan triangle

TL;DR

This paper explores the relationship between Tuenter polynomials and Catalan triangle numbers, revealing new coefficient expressions and polynomial-based descriptions.

Contribution

It introduces a novel connection between Tuenter polynomials and Catalan triangle coefficients, expanding understanding of their combinatorial structure.

Findings

Coefficients of Tuenter polynomials are expressed via Catalan triangle numbers.

A new triangle of coefficients is described using certain polynomials.

The paper provides a polynomial-based description of these coefficients.

Abstract

We consider Tuenter polynomials as linear combinations of descending factorials and show that coefficients of these linear combinations are expressed via a Catalan triangle of numbers. We also describe a triangle of coefficients in terms of some polynomials.