We show that there is an (amazing!) integer valued function f(n) (n=0,1,2,...) such that 

(a) the sequence f(0)/f(1), f(1)/f(2), f(2)/f(3), ... consists of all of the positive rational numbers, each occurring once and     only once, and 
(b) f(n) and f(n+1) are always relatively prime, so each rational occurs in part (a) in reduced form, and 
(c) the function f(n) actually counts something of combinatorial interest.