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Let Formula: see text denote the second-order harmonic number Formula: see text for n = 0, 1, 2, …. In this paper we obtain the following identity: Formula: see text We explain how we found the series and develop related congruences involving Bernoulli or Euler numbers; for example, it is shown that Formula: see text for any prime p > 3, where E 0 , E 1 , E 2 , … are Euler numbers. Motivated by the Amdeberhan–Zeilberger identity Formula: see text, we also establish the congruence Formula: see text for each prime p > 3.
Zhi‐Wei Sun (Mon,) studied this question.