  In this paper we resolve a conjecture of Kresch and Tamvakis. Our result is
the following.
  Theorem: For any positive integer $D$ and any integers $i,j$ $(0\leq i,j \leq
D)$, the absolute value of the following hypergeometric series is at most 1:
\begin{equation*}
  {_4F_3} \left[ \begin{array}{c} -i, \; i+1, \; -j, \; j+1 \\ 1, \; D+2, \; -D
\end{array} ; 1 \right].
  \end{equation*}
  To prove this theorem, we use the Biedenharn-Elliott identity, the theory of
Leonard pairs, and the Perron-Frobenius theorem.
