\documentclass[12pt]{article}

\usepackage{amssymb}
\usepackage{amsmath}
\usepackage{amsthm}
\usepackage{amsfonts}
 
\def \RM{\mathbb{R}}%        corps des reels
\def \NM{\mathbb{N}}%        entiers naturels
\def \ZM{\mathbb{Z}}%        entiers relatifs
\def \CM{\mathbb{C}}%        nombres complexes
\def \QM{\mathbb{Q}}%        nombres rationnels
 
\begin{document}

\begin{abstract}
Given a sequence $x=\{x_n, \ n \in \NM \}$ with integer values, or more
generally with values in a ring of polynomials with integer
coefficients, one can form the {\it generalized binomial coefficients}
associated with $x$,  ${\binom nm}_x=\prod_{l=1}^{m} \frac{x_{n-l+1}}{x_l}$.
In this note we introduce several sequences that possess the following 
remarkable feature: the fractions $\binom nm_x$ are in fact polynomials with
integer coefficients.
\end{abstract}

\end{document}




