Let $n, m \in \mathbb{N}$ each be a D996: Natural number.
The Bell coefficient with respect to $(n, m)$ is the D996: Natural number \begin{equation} {n \brace m} : = \# \left\{ P : P \text{ properly partitions } \{ 1, \ldots, n \} \text{ and } |P| = m \right\} \end{equation}

Let $n, m \in \mathbb{N}$ each be a D996: Natural number such that

(i)	$\text{Part} \{ 1, \ldots, n \}$ is the D2910: Set of proper set partitions for $\{ 1, \ldots, n \}$

The Bell coefficient with respect to $(n, m)$ is the D996: Natural number \begin{equation} {n \brace m} : = \# \left\{ P \in \text{Part} \{ 1, \ldots, n \} : |P| = m \right\} \end{equation}