  To a crystallographic root system \Phi, and a positive integer k, there are
associated two Fuss-Catalan objects, the set of nonnesting partitions
NN^(k)(\Phi), and the cluster complex \Delta^(k)(\Phi). These posess a number
of enumerative coincidences, many of which are captured in a surprising
identity, first conjectured by Chapoton for k=1 and later generalized to k>1 by
Armstrong. We prove this conjecture, obtaining some structural and enumerative
results on NN^(k)(\Phi) along the way, including an earlier conjecture by Fomin
and Reading giving a refined enumeration by Fu{\ss}-Narayana numbers.
