  We analyze the nonequilibrium transport properties of a quantum dot with a
harmonic degree of freedom (Holstein phonon) coupled to metallic leads, and
derive its full counting statistics (FCS). Using the Lang-Firsov (polaron)
transformation, we construct a diagrammatic scheme to calculate the cumulant
generating function. The electron-phonon interaction is taken into account
exactly, and the employed approximation represents a summation of a diagram
subset with respect to the tunneling amplitude. By comparison to Monte Carlo
data the formalism is shown to capture the basic properties of the strong
coupling regime.
