\begin{definition}[Definition:Binomial Coefficient/Integers/Definition 3]
Let $n \in \Z_{\ge 0}$ and $k \in \Z$.
Then the '''binomial coefficient''' $\dbinom n k$ is defined as the coefficient of the term $a^k b^{n - k}$ in the expansion of $\paren {a + b}^n$.
\end{definition}