We present several congruences modulo a power of prime $p$ concerning sums ofthe following type $\sum_{k=1}^{p-1}{m^k\over k^r}{2k\choose k}^{-1}$ whichreveal some interesting connections with the analogous infinite series.
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机译：对于以下类型的总和，我们给出了以质数$ p $的幂为模的同余项，其中$ \ sum_ {k = 1} ^ {p-1} {m ^ k \ over k ^ r} {2k \ choose k} ^ {- 1} $与相似的无限级数揭示了一些有趣的联系。
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