  By employing a numerical renormalization group technique, we evaluate
electronic specific heat coefficient $\gamma$ of the Anderson model coupled
with local anharmonic phonons for the oscillation of a caged atom. For the
rattling-type cage potential with a flat and wide region in the bottom, we find
that phonon-mediated attraction is largely enhanced. When the potential shape
is deformed from the rattling type, there occurs a cancellation between Coulomb
repulsion and the phonon-mediated attraction. In such a situation, spin and
charge fluctuations are comparable to each other, leading to the realization of
exotic electron-phonon complex state with large and magnetically robust
$\gamma$.
