  We study the Jacobi-Trudi-type determinant which is conjectured to be the
q-character of a certain, in many cases irreducible, finite-dimensional
representation of the quantum affine algebra of type C_n. Like the D_n case
studied by the authors recently, applying the Gessel-Viennot path method with
an additional involution and a deformation of paths, we obtain a positive sum
expression over a set of tuples of paths, which is naturally translated into
the one over a set of tableaux on a skew diagram.
