  We study the compatibility between the antipode and the preLie product of a
Com-PreLie Hopf algebra, that is to say a commutative Hopf algebra with a
complementary preLie product, compatible with the product and the coproduct in
a certain sense. An example of such a Hopf algebra is the Connes-Kreimer Hopf
algebra, with the preLie product given by graftingof forests, extending the
free preLie product of grafting of rooted trees. This compatibility is then
used to study the antipode of the Connes-Moscovici subalgebra, whichcan be
defined with the help of this preLie product. The antipode of the generators of
this subalgebra gives a family of combinatorial coefficients indexed by
partitions,which can be computed with the help of iterated harmonic sums.
