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In this paper we obtain the following identity: $$\\sum_{k=1}^\\infty\\frac{2^kH_{k-1}^{(2)}}{k\\binom{2k}k}=\\frac{\\pi^3}{48}.$$ We explain how we found the series and develop related congruences involving Bernoulli or Euler numbers; for example, it is shown that $$\\sum_{k=1}^{p-1}\\frac{\\binom{2k}k}{2^k}H_k^{(2)}\\equiv-E_{p-3}\\pmod{p}$$ for any prime $p>3$, where $E_0,E_1,E_2,\\ldots$ are Euler numbers. 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In this paper we obtain the following identity: $$\\sum_{k=1}^\\infty\\frac{2^kH_{k-1}^{(2)}}{k\\binom{2k}k}=\\frac{\\pi^3}{48}.$$ We explain how we found the series and develop related congruences involving Bernoulli or Euler numbers; for example, it is shown that $$\\sum_{k=1}^{p-1}\\frac{\\binom{2k}k}{2^k}H_k^{(2)}\\equiv-E_{p-3}\\pmod{p}$$ for any prime $p>3$, where $E_0,E_1,E_2,\\ldots$ are Euler numbers. 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