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.
The numerator of this fraction is defined as the elementary symmetric polynomial of degree k in the variables a1 through an, which involves taking the sum of all possible products of k of these variables, listed in increasing numerical order.