What does this summation do?

I was given this summation today and asked to find out what it did. So far my friend and I have run into a brick wall at every turn.

Here's the summation:

$\displaystyle

\sum_{i=1}^N\sum_{j=i+1}^N \frac{a_i a_j}{N(N-1)/2}

$

This is the only information we were given, and we interpreted $\displaystyle a_i$ and $\displaystyle a_j$ as being integers in some set of N integers, where the first integer in the set is $\displaystyle a_1$

The problem we've run into is that when i gets to be N, j = N+1 and $\displaystyle a_j$ is therefore undefined. So we've been interpreting it as i goes from 1 to N-1. Does anyone recognize this as a famous series of some sort, or know what it does?

Thanks for any information anyone can provide,

-Ben