  The influence of carbon deficiency on superconductivity of MgCNi$_{3}$ is
investigated by specific heat measurements in the normal and superconducting
state. In order to perform a detailed analysis of the normal state specific
heat, a computer code is developed which allows for an instantaneous estimate
of the main features of the lattice dynamics. By analyzing the evolution of the
lattice vibrations within the series and simultaneously considering the visible
mass enhancement, the loss in the electron-phonon coupling can be attributed to
significant changes of the prominent Ni vibrations. The present data well
supports the recently established picture of strong electron-phonon coupling
and ferromagnetic spin fluctuations in this compound.
