Školjka

Let $n \geq 2$ be an integer, and let $A_n$ be the set $$ A_n = \{ 2^n - 2^k \, | \, k \in \mathbb{Z}, 0 \leq k < n \} \text{.} $$ Determine the largest positive integer that cannot be written as the sum of one or more (not necessarily distinct) elements of $A_n$. \begin{flushright}\emph{(Serbia)}\end{flushright}