  A multi-parafermion basis of states for the Z_k parafermionic models is
derived. Its generating function is constructed by elementary steps. It
corresponds to the Andrews multiple-sum which enumerates partitions whose parts
separated by the distance k-1 differ by at least 2. Two analogous bases are
derived for graded parafermions; one of these entails a new expression for
their fermionic characters.
