We spectroscopically studied the population of the excited hydrogen atomic states with the principal quantum numbers n = 3 and 4 in a decaying plasma produced by a pulsed discharge in a mixture of helium (p = 40.4 Torr) with a small amount of hydrogen ([H₂] ≈ 10¹² cm^-3). Experiments on recording the response of the spectral line intensities to a short-duration electron temperature perturbation revealed the contribution of electron-ion recombination to the population of the H*(n = 3) states in the early afterglow. The ions produced by collisions of hydrogen molecules with metastable He(2³S₁) atoms, whose density decreases relatively rapidly with time in the decaying plasma, were assumed to be involved in this process. No population of the H*(n = 4) atomic levels due to electron-ion recombination was found. Our experimental results are consistent with the conclusions of previous studies that excitation transfer during collisions of metastable helium molecules with hydrogen molecules plays a major role in the population of the excited hydrogen atomic states both with n = 3 and with n = 4 during most of the afterglow.