Definition:Multinomial Coefficient/Trinomial

Let $k_1, k_2, k_3 \in \Z_{\ge 0}$ be positive integers.
The trinomial coefficient of $k_1, k_2, k_3$ is a particular case of a multinomial coefficient, defined as:
$\dbinom {k_1 + k_2 + k_3} {k_1, k_2, k_3} := \dfrac {\left({k_1 + k_2 + k_3}\right)!} {k_1! \, k_2! \, k_3!}$