Enumerate

To enumerate a set of objects satisfying some set of properties means to explicitly produce a listing of all such objects. The problem of determining or counting all such solutions is known as the enumeration problem.

A generating function

is said to enumerate  (Hardy 1999, p. 85).

REFERENCES:

Hardy, G. H. Ramanujan: Twelve Lectures on Subjects Suggested by His Life and Work, 3rd ed. New York: Chelsea, 1999.