Definition:Binomial Coefficient/Integers/Definition 1

Definition
Let $n \in \Z_{\ge 0}$ and $k \in \Z$.

Then the symbol $\dbinom n k$ is interpreted as:


 * $\dbinom n k = \begin{cases}

\dfrac {n!} {k! \left({n - k}\right)!} & : 0 \le k \le n \\ & \\ 0 & : \text { otherwise } \end{cases}$

The number $\dbinom n k$ is known as a binomial coefficient.

Also see

 * Equivalence of Definitions of Binomial Coefficient