Definition:Multinomial Coefficient

Definition
Let $k_1, k_2, \ldots, k_m \in \Z_{\ge 0}$ be positive integers.

The multinomial coefficient of $k_1, \ldots, k_m$ is defined as:
 * $\dbinom {k_1 + k_2 + \cdots + k_m} {k_1, k_2, \ldots, k_m} := \dfrac {\left({k_1 + k_2 + \cdots + k_m}\right)!} {k_1! \, k_2! \, \ldots k_m!}$