  Chapuy and Stump have given a nice generating series for the number of
factorisations of a Coxeter element as a product of reflections. Their method
is to evaluate case by case a character-theoretic expression. The goal of this
note is to give a uniform evaluation of their character-theoretic expression in
the case of Weyl groups, by using combinatorial properties of Deligne-Lusztig
representations.
