\begin{definition}[Definition:Binomial Coefficient/Integers/Definition 1]
Let $n \in \Z_{\ge 0}$ and $k \in \Z$.
Then the '''binomial coefficient''' $\dbinom n k$ is defined as:
:$\dbinom n k = \begin{cases}
\dfrac {n!} {k! \paren {n - k}!} & : 0 \le k \le n \\
& \\
0 & : \text { otherwise } \end{cases}$
where $n!$ denotes the factorial of $n$.
\end{definition}