[Value = 9 points]
Let {a1, a2, ..., an} be a set of real numbers, such that a1 < a2 < ... < an. We define the power sum of {a1, a2, ..., an} to be a1i1 + a2i2 + ... + anin.
Given any n, let Sn be the sum of the power sums of all non-empty subsets of the set {1,2,...,n}.
S8 is -176 - 64i. What is S9?
