Renyi entropies and C_T for higher derivative free scalars and spinors on even spheres

General expressions for the R'enyi entropies and central charges for higher derivative free spinors and scalars on even spheres are obtained using a direct spectral method on a compact lune division of the sphere. Formulae and numbers are rapidly obtained for any dimension and order of derivative. The relation between the conformal anomaly and the hyperbolic free energy is briefly explored using standard expansions. A field theoretic derivation of the central charge formula for higher derivative scalars in any (even) dimension, given by Osborn and Stergiou and by Gliozzi {\it et al}, is thereby provided. The corresponding extension to spinors is made. Generalised Bernoulli polynomials play an important technical role.