Holographic multiple-input multiple-output (HMIMO) communication systems utilize spatially-constrained massive MIMO arrays containing large numbers of antennas with sub-wavelength spacing, and have emerged as a promising candidate technology for Sixth Generation (6G) networks. In this paper, we consider the downlink of a multi-user HMIMO communication system under a Fourier plane-wave series representation of the stochastic electromagnetic MIMO channel model, and make two important contributions. First, we present a closed-form expression of the ergodic achievable downlink rate under maximum ratio transmission (MRT) precoding at the base station (BS). The derived expression explicitly shows the effect of the side-lengths of the HMIMO surfaces at the BS and each user, and the number of antennas deployed in these surfaces on the user rates. Second, we formulate an energy efficiency (EE) maximization problem with respect to the number of antennas arranged within spatially-constrained HMIMO surfaces at the BS and each user. The resulting implicit solution for this problem is shown to be globally optimal. Numerical results yield useful insights into the EE performance of multi-user HMIMO systems in different operating regimes.