  We theoretically investigate effects of quantum fluctuation between even and
odd charge states on the transport properties of a
normal-superconducting-normal single-electron tunneling transistor. The charge
fluctuation is discussed beyond the orthodox theory. We find that the charging
energy renormalization enhances the parity effect: The Coulomb blockade regime
for odd state is reduced and that for even state is widened. We show that the
renormalization factor can be obtained by measuring the peak position of the
conductance. The renormalization factor reduces with increasing the applied
bias voltage.
