Radiative recombination of O+ generates a variety of O-atom Rydberg levels, which then radiatively cascade to the ground state. The last two steps in the cascade produce 844.6 nm and 130.2--130.6 nm radiation in the triplet set of Rydberg levels and 777.2--777.5 nm and 135.6 nm radiation in the quintets. These four emissions are well known from ionospheric observations, and the higher members of the cascades are sometimes seen in auroral spectra but rarely in the nightglow. Sky spectra taken in 2000 at the Keck II telescope with the ESI echelle spectrograph reveal 20 members of the Rydberg transitions in the 390--930 nm region not previously observed in the nightglow. Most of these are not seen in earlier Keck spectra, taken at solar minimum. We are able to quantify the relative intensities of the emissions across the entire wavelength region using standard star spectra, allowing comparisons to be made with theoretical calculations. As the atmosphere is optically thin for the quintet transitions, corrections for radiative scattering are not necessary, and relative agreement between theory and observations is excellent. For the triplets the data agree more closely with the optically thick calculations. The relationship between the intensities of the quintet 3d-3p (926--926.6 nm) and the triplet 3p-3s (844.6 nm) multiplets is investigated and found to be linear. Accurate wavelengths are determined for the Rydberg quintets on the basis of observations with the high-resolution (~40,000) Keck I/HIRES system. For the triplets the multiplets are incompletely resolved. Examples of spectra are presented where the 844.6 nm multiplet is the only OI Rydberg emission observed. We argue that the cause is Bowen fluorescence, a consequence of photoexcitation of the OI 3d-2p transition by H Lyman-¿ radiation in the geocorona. The fact that so many of the oxygen Rydberg lines have been identified in this study and that their intensities are consistent with cascade models of radiative recombination is a strong confirmation of the importance of this process in the tropical nightglow near solar maximum.