ISL 2014 N1

Let $n \geqslant 2$ be an integer, and let $A_{n}$ be the set $$A_{n}=\left\{2^{n}-2^{k} \mid k \in \mathbb{Z}, 0 \leqslant k<n\right\} .$$ Determine the largest positive integer that cannot be written as the sum of one or more (not necessarily distinct) elements of $A_{n}$. (Serbia)