On the divisibility of some truncated hypergeometric series

Let $p$ be an odd prime and $r\geq 1$. Suppose that $\alpha $ is a $p$-adic integer with $\alpha \equiv 2a\pmod p$ for some $1\leq a \lt (p+r)/(2r+1)$. We confirm a conjecture of Sun and prove that $${}_{2r+1}F_{2r}\biggl [\begin {matrix}\alpha &\alpha &\