Math Time problem proposal

will mean the sum of the values f (i1, i2, ..., ik) over all ”good” k-tuples (i1, i2, ..., ik) ; hereby, a k-tuple (i1, i2, ..., ik) is called ”good” if it satisfies iu ∈ {1, 2, ..., n} for every u ∈ {1, 2, ..., k} and also satisfies all the assertions A1, A2, ..., Al. Using this notation, we can write many typical sums in a simpler form: For instance, ∑ 1≤i≤n f (i) = i ∑ f (i) , and ∑ 1≤i<j≤n f (i, j) = i, j ∑