  For a noncentrosymmetric superconductor such as Y$_2$C$_3$, we consider a
parity-mixing model composed of spin-singlet s-wave and spin-triplet f-wave
pairing components.
  The $d$-vector in f-wave state is chosen to be parallel to the Dresselhaus
asymmetric spin-orbit coupling vector.
  It is found that, the quasiparticle excitation spectrum exhibits distinct
nodal structure as a consequence of parity-mixing. Our calculation predict
anomalous noninteger power laws for low-temperature nuclear spin-lattice
relaxation rate $T_{1}^{-1}$.
  We demonstrate particularly that such a model can qualitatively account for
the existing experimental results of the temperature dependence of $T_{1}^{-1}$
in Y$_2$C$_3$.
