On the coefficients of the distinct monomials in the expansion of $x_1(x_1+x_2)\cdots(x_1+x_2+\cdots+x_n)$

TL;DR

This paper investigates the coefficients of distinct monomials in a specific multivariate polynomial expansion, focusing on their maximal values and properties.

Contribution

It introduces the study of these coefficients and provides new results concerning their maximal coefficients in the polynomial expansion.

Findings

Identification of the maximal coefficients of monomials

Results on the distribution of coefficients

Foundational insights into polynomial coefficient behavior

Abstract

We initiate the study of the coefficients of the distinct monomials in the expansion of the multivariate polynomials $x_1(x_1+x_2)\cdots(x_1+x_2+\cdots+x_n), n\in\N$. In particular we obtain several results regarding their maximal coefficients.