Comments on: Victor Reiner, The distribution of descents and length in a Coxeter group
Raphael Rouquier pointed out the following relevant reference:
I. G. Macdonald, "The Poincare series of a Coxeter Group",
Math. Ann. 199 (1972), 161-174. In particular, formulas
(12) and (14) of the present paper are stated on page 173
of this reference.