I am looking for a way to either 1) simplify the following equation or 2) provide a reasonably tight upper bound to the following. Note that $\epsilon < 1$, and reasonably also $\epsilon \ll 1$.
\begin{equation} \frac{2}{(l + 2)!} \sum_{h = 0}^{l} s_2(l, h) (1 - \epsilon)^{2^h} \end{equation}
where $s_2(l, h)$ refers to the unsigned 2-Stirling number of the first kind. A table of these values is linked [here]https://oeis.org/A143491/table. Would really appreciate any help!
