  It is shown that a refined version of a q-analogue of the Eulerian numbers
together with the action, by conjugation, of the subgroup of the symmetric
group $S_n$ generated by the $n$-cycle $(1,2,...,n)$ on the set of permutations
of fixed cycle type and fixed number of excedances provides an instance of the
cyclic sieving phenonmenon of Reiner, Stanton and White. The main tool is a
class of symmetric functions recently introduced in work of two of the authors.
