On a sequence of polynomials with hypothetically integer coefficients

TL;DR

This paper proves that a specific recursively defined sequence of polynomials has integer coefficients, confirming a long-standing hypothesis about their integrality.

Contribution

It provides a proof of the integrality of coefficients for a particular polynomial sequence previously conjectured.

Findings

Coefficients of the polynomial sequence are integers.

The recursive definition leads to integrality of all coefficients.

Supports the hypothesis of integer coefficients in the sequence.

Abstract

The first author introduced a sequence of polynomials (\cite{8}, sequence A174531) defined recursively. One of the main results of this study is proof of the integrality of its coefficients.