  Let a_n(k) be the kth coefficient of the nth cyclotomic polynomial Phi_n(x).
As n ranges over the integers, a_n(k) assumes only finitely many values. For
any such value v we determine the density of integers n such that a_n(k)=v.
Also we study the average of the a_n(k). We derive analogous results for the
kth Taylor coefficient of 1/Phi_n(x) (taken around x=0), the kth coefficient of
the nth reciprocal cyclotomic polynomial. We formulate various open problems.
