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We present the first detection of the H40a, H34a and H31a radio recombination lines (RRLs) at millimeter wavelengths toward the high-velocity, ionized jet in the Cepheus A HW2 star forming region. From our single-dish and interferometric observations, we find that the measured RRLs show extremely broad asymmetric line profiles with zero-intensity linewidths of ~1100 kms-1. From the linewidths, we estimate a terminal velocity for the ionized gas in the jet of >500 kms-1, consistent with that obtained from the proper motions of the HW2 radio jet. The total integrated line-to-continuum flux ratios of the H40a, H34a and H31a lines are 43, 229 and 280 kms-1, clearly deviating from LTE predictions. These ratios are very similar to those observed for the RRL maser toward MWC349A, suggesting that the intensities of the RRLs toward HW2 are affected by maser emission. Our radiative transfer modeling of the RRLs shows that their asymmetric profiles could be explained by maser emission arising from a bi-conical radio jet with a semi-aperture angle of 18 deg, electron density distribution varying as r^(-2.11) and turbulent and expanding wind velocities of 60 and 500 kms-1.