The population of excited states of the hydrogen atom in an afterglow plasma produced by a pulsed discharge in helium (40 Torr) with a small admixture of hydrogen ([H₂] ≈ 10¹² cm^-3) has been studied spectroscopically. The contribution from electron-ion recombination Γ ₃^rec to the production rate of atoms H(n = 3) has been separated. On the basis of an experiment in which the response of the spectral line intensities to the perturbation of the electron temperature in the afterglow phase was observed, the dependence Γ ₃^rec (T_e)∼T_e^-(0.9-1.0) has been obtained in the region kT_e = 0.026-0.064 eV.