World Scientific Publishing, International Journal of Mathematics, 08(26), p. 1550055, 2015
DOI: 10.1142/s0129167x1550055x
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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 E0, E1, E2, … 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.