  We study a family of higher-derivative conformal operators $P_{2k}^{(2)}$
acting on transverse-traceless symmetric 2-tensors on generic Einstein spaces.
They are a natural generalization of the well-known construction for scalars.
  We first provide the alternative description in terms of a bulk
Poincar\'e-Einstein metric by making use of the AdS/CFT dictionary and argue
that their holographic dual generically consists of bulk massive gravitons. At
one-loop quantum level, we put forward a holographic formula for the functional
determinant of the higher-derivative conformal operators $P_{2k}^{(2)}$ in
terms of the functional determinant for massive gravitons with standard and
alternate boundary conditions. The analogous construction for vectors
$P_{2k}^{(1)}$ is worked out as well and we also rewrite the holographic
formula for unconstrained vector and traceless symmetric 2-tensor by decoupling
the longitudinal part.
  Finally, we show that the holographic formula provides the necessary building
blocks to address the massless and partially massless bulk gravitons. This is
confirmed in four and six dimensions, verifying full agreement with results
available in the literature.
