  Phonon-assisted electronic tunnelings through a vibrating quantum dot
embedded between normal and superconducting leads are studied in the Kondo
regime. In such a hybrid device, with the bias applied to the normal lead, we
find a series of Kondo sidebands separated by half a phonon energy in the
differential conductance, which are distinct from the phonon-assisted sidebands
previously observed in the conventional Andreev tunnelings and in systems with
only normal leads. These Kondo sidebands originate from the Kondo-Andreev
cooperative cotunneling mediated by phonons, which exhibit a novel Kondo
transport behavior due to the interplay of the Kondo effect, the Andreev
tunnelings, and the mechanical vibrations. Our result could be observed in a
recent experiment setup [J. Gramich \emph{et al.}, PRL \textbf{115}, 216801
(2015)], provided that their carbon nanotube device reaches the Kondo regime at
low temperatures.
