  We present a combined experimental and theoretical study of resonant Raman
spectroscopy in single- and triple-layer MoTe$_2$. Raman intensities are
computed entirely from first principles by calculating finite differences of
the dielectric susceptibility. In our analysis, we investigate the role of
quantum interference effects and the electron-phonon coupling. With this
method, we explain the experimentally observed intensity inversion of the
$A^\prime_1$ vibrational modes in triple-layer MoTe2 with increasing laser
photon energy. Finally, we show that a quantitative comparison with
experimental data requires the proper inclusion of excitonic effects.
