Study on Morgan-Voyce type polynomials with Euler-Seidel algorithm

Abstract

This paper bridges the domains of degenerate special polynomials, the Euler-Seidel matrix method, and Morgan-Voyce polynomials. We introduce two new families of Morgan-Voyce type polynomials and establish their structural properties, including explicit formulas and recurrence relations. Additionally, we define three polynomial variants and prove that three distinct binomial-type sums for Bell polynomials can be expressed as finite sums involving these new families, and derive their exponential generating functions. We then construct Euler-Seidel matrices using the initial sequences associated with Morgan-type polynomials. Our results yield novel algebraic identities and expand the application of matrix methods in combinatorial analysis.