On some theorems in the theory of numbers
R. E. Allardice · Proceedings of the Edinburgh Mathematical Society · 1889
The number of groups of n which may be selected from 2n is 2n(2n − l)…(n + l)/n! But make the 2n into two groups of n, and select r out of the first and n − r out of the second. This gives [n(n−l)…(n−r+l)/r!] + [n(n−l)…(r + l)/(n−r)!] ways of thus making a group of n. Hence