\documentclass[12pt]{article}

\newcommand{\ff}[2]{ \ensuremath{ {#1}^{\underline{#2}} }}		

\begin{document}

\begin{abstract}
We investigate the coefficients generated by expressing the falling
factorial $\ff{(xy)}{k}$ as a linear combination of falling factorial
products $\ff{x}{l}\ff{y}{m}$ for $l,m =1, \dots, k$. Algebraic and
combinatoric properties are discussed, some in relation to Stirling
numbers.
\end{abstract}

\end{document}
