Single electron hydrogen or hydrogenic ions have analytical forms to evaluate the atomic parameters for the inverse processes of photoionization and electron-ion recombination (H I + hν↔ H II + e) where H is hydrogen. Studies of these processes have continued until the present day (i) as the computations are restricted to lower principle quantum number n and (ii) to improve the accuracy. The analytical expressions have many terms and there are numerical instabilities arising from cancellations

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... f terms. Strategies for fast convergence of contributions were developed but precise computations are still limited to lower n. This report gives a brief review of the earlier precise methodologies for hydrogen, and presents numerical tables of photoionization cross sections (σPI), and electron-ion recombination rate coefficients (αRC) obtained from recombination cross sections (σRC) for all n values going to a very high value of 800. σPI was obtained using the precise formalism of Burgess and Seaton, and Burgess. αRC was obtained through a finite integration that converge recombination exactly as implemented in the unified method of recombination of Nahar and Pradhan. Since the total electron-ion recombination includes all levels for n = 1–∞, the total asymptotic contribution of n = 801–∞, called the top-up, is obtained through a n−3 formula. A FORTRAN program "hpxrrc.f" is provided to compute photoionization cross sections, recombination cross sections and rate coefficients for any nl. The results on hydrogen atom can be used to obtain those for any hydrogenic ion of charge z through z-scaling relations provided in the theory section. The present results are of high precision and complete for astrophysical modelings.