  Let $H(p)$ be the set of 2-bridge knots $K$ whose group $G$ is mapped onto a
non-trivial free product, $Z/2 * Z/p$, $p$ being odd. Then there is an
algebraic integer $s_0$ such that for any $K$ in $H(p)$, $G$ has a parabolic
representation $\rho$ into $SL(2, Z[s_0]) \subset SL(2,C)$. Let $\Delta(t)$ be
the twisted Alexander polynomial associated to $\rho$. Then we prove that for
any $K$ in $H(p)$, $\Delta(1)=-2s_0^{-1}$ and $\Delta(-1)=-2s_0^{-1}\mu^2$,
where $s_0^{-1}, \mu \in Z[s_0]$. The number $\mu$ can be recursively
evaluated.
