I have seen notation like this, commonly in regard to matrix multiplication:
$$ b_i = \sum_{j \ne i} A_{ij} x_j $$
So this is a matrix multiplication that excludes the diagonal ($j=i$).
I'm kind of confused when it's ok to just leave off specification of the upper limit or lower limit from the sum. From here, I'm assuming if you have an exclusion, you're supposed to sum over all elements not excluded?