1983 AIME Problem 13

For \{1, 2, 3, \ldots, n\} and each of its nonempty subsets a unique alternating sum is defined as follows. Arrange the numbers in the subset in decreasing order and then, beginning with the largest, alternately add and subtract succesive numbers. For example, the alternating sum for \{1, 2, 3, 6,9\} is 9-6+3-2+1=5 and for \{5\} it is simply 5. Find the sum of all such alternating sums for n=7.

Leading zeroes must be inputted, so if your answer is 34, then input 034

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.