  We calculate the one-loop partition function for a massless arbitrary-spin
field on quotients of a general dimensional AdS background using the results of
arXiv:1103.3627. We use these results to compute the one-loop partition
function for a Vasiliev theory in AdS_5. An interesting form of the answer,
suggestive of a vacuum character of an enhanced symmetry algebra is obtained.
We also observe a close connection between the partition function for this
Vasiliev theory and the d-dimensional MacMahon function.
