= Falling factorial
{title2=$(t)_j=t(t-1)\cdots(t-j+1)$}
The falling factorial is the product of $j$ successive descending factors, with $(t)_0=1$. Another notation is $t^{\underline j}$; this article uses $(t)_j$ for descending factors, whereas the <rising factorial> uses the same notation for ascending factors. For a nonnegative integer $t$, it counts ordered selections of $j$ distinct objects and vanishes when $j>t$. Powers expand as $t^j=\sum_{\ell=0}^j S(j,\ell)(t)_\ell$, where $S(j,\ell)$ is a <Stirling number of the second kind>.
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