  We analytically compute the Renyi entropies for the RSOS models, representing
a wide class of exactly solvable models with multicritical conformal points
described by unitary minimal models and $\mathbb{Z}_n$ parafermions. The exact
expressions allow for an explicit comparison of the expansions around the
critical points with the predictions coming from field theory. In this way it
is possible to point out the nature of the so-called "unusual corrections",
clarifying the link with the operator content, the role of the symmetries and
the boundary conditions. By choosing different boundary conditions, we can
single out the ground states as well as certain combinations of high energy
states. We find that the {\it entanglement spectrum} is given by operators that
are not present in the bulk Hamiltonian, although they belong to the same
representation of a Virasoro Algebra. In the parafermionic case we observe
unexpected logarithmic corrections.
