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Let 
$p>3$ be a prime and let 
$a$ be a rational 
$p$-adic integer with 
$a\not \equiv 0\;(\text{mod}\;p)$. We evaluate modulo 
$$\begin{eqnarray}\mathop{\sum }_{k=1}^{(p-1)/2}\frac{1}{k}\binom{a}{k}\binom{-1-a}{k}\quad \text{and}\quad \mathop{\sum }_{k=0}^{(p-1)/2}\frac{1}{2k-1}\binom{a}{k}\binom{-1-a}{k}\end{eqnarray}$$
$p^{2}$ in terms of Bernoulli and Euler polynomials.
