  In non-centrosymmetric superconductors, spin-orbit coupling can induce an
unconventional superconducting state with a mixture of s-wave spin-singlet and
p-wave spin-triplet channels, which leads to a variety of exotic phenomena,
including anisotropic upper critical field, magnetoelectric effect, topological
superconductivity, et al. It is commonly thought that inversion symmetry
breaking is substantial for pairing-mixed superconducting states. In this work,
we theoretically propose that a new type of pairing-mixed state, namely the
mixture of s-wave spin-singlet and d-wave spin-quintet channels, can be induced
by spin-orbit coupling even in the presence of inversion symmetry when
electrons effectively carry "spin-3/2" in superconductors. As a physical
consequence of the singlet-quintet pairing mixing, topological nodal-line
superconductivity is found in such system and gives rise to flat surface
Majorana bands. Our work provides a possible explanation of unconventional
superconducting behaviors observed in superconducting half-Heusler compounds.
