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

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