On Pellnomial coefficients and Pell-Catalan numbers

Abstract

In this paper, we first give the Pascal’s identity for Pellnomial coefficients and then we show that the Pellnomial coefficients are integers. We obtain that the product of r consecutive Pell numbers is divisible by the Pell analog of r!. Also, we introduce the divisibility theorems between Pell numbers and Pellnomial coefficients. Furthermore, we first define Pell–Catalan numbers and then we derive two formulas for presenting Pell–Catalan numbers.