# Show that $\sum_{i=0}^{\frac{p-1}{2}} {{\frac{p-1}{2}}\choose {i}}^2 x^{\frac{p-1}{2}-i}$ is separable

I want to show that $\sum_{i=0}^{\frac{p-1}{2}} {{\frac{p-1}{2}}\choose {i}}^2 x^{\frac{p-1}{2}-i}$ is a separable polynomial over this field.Start with $\binom{\frac{p-1}2}i\equiv_p\binom{2i}i4^{-i} \mod p$.