The numerator of this fraction is the elementary symmetric polynomial of degree k in the n variables a1, a2, ..., an, that is, the sum of all products of k of the numbers a1, a2, ..., an with the indices in increasing order.
In algebraic terms, the numerator of this fraction represents the elementary symmetric polynomial of degree k in the variables a1 through an, which involves calculating the sum of all possible products of k numbers from this set, arranged in increasing numerical order.