Generalization of Wolstenholme's and Morley's congruences

In this paper, we show that for any prime $p\geq 11$ and any $p$-integer $\alpha$, we have $\binom{\alpha p-1}{p-1}\equiv1-\alpha(\alpha-1)(\alpha^2-\alpha-1)p\sum_{k=1}^{p-1}\frac{1}{k}+\alpha^2(\alpha-1)^2 p^2\sum_{1\leq i<j\leq p-1}\frac{1}{ij}\pmod{p^7}$. This congruence generalizes the congruences of Wolstenholme, Morley, Glaisher, Carlitz, McIntosh, Tauraso and Meštrović. Furthermore, it allows to rediscover the congruences of Glaisher, Carlitz and Zhao in a simple way.