Let \( S \) be an \( (n+1) \times (n+1) \) matrix defined by
\[
S_{ij} = \begin{cases}
(n+1)-i & \text{ if } j=i+1, \\
i-1 & \text{ if } j=i-1, \\
0 & \text{ otherwise. }
\end{cases}
\]
Find all eigenvalues of \( S \).