  Let g be a free brace algebra. This structure implies that g is also a prelie
algebra and a Lie algebra. It is already known that g is a free Lie algebra. We
prove here that g is also a free prelie algebra, using a description of g with
the help of planar rooted trees, a permutative product, and anipulations on the
Poincar\'e-Hilbert series of g.
