Let S be a set of some positive integers.

We'll call S autonomous if the number of elements in S is itself an element of S. e.g. the set {2,3,5} is autonomous, as is the set {2,7}, but the sets {1, 4} or {2,4,5} are not.

Determine a general formula for the number

of autonomous subsets of {1, 2, 3, ... , n}.