Is the value of the following summation can be expressed in a closed form?
$$ \Delta = \sum_{k=0}^{n} S(n,k) \; (C)_k \; m^k $$
where $S(n,k)$ is Stirling number of second kind, $(C)_k$ is the falling factorial defined as $(C)_k:=C(C-1)\cdots (C-k+1)$ and $ 0< m <1$.