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A266560
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Decimal expansion of the generalized Glaisher-Kinkelin constant A(14).
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19
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1, 3, 3, 8, 6, 4, 4, 7, 5, 4, 2, 4, 1, 5, 3, 6, 2, 9, 9, 5, 5, 8, 0, 4, 6, 9, 5, 8, 8, 7, 3, 2, 5, 5, 1, 4, 2, 5, 4, 2, 0, 9, 2, 5, 3, 7, 0, 6, 2, 7, 4, 2, 4, 8, 0, 2, 3, 4, 0, 6, 2, 0, 9, 4, 5, 8, 9, 7, 9, 5, 3, 1, 5, 2, 8, 5, 1, 9, 6, 4, 8, 4, 5, 5, 2, 4, 5, 2, 9, 3, 1, 3, 9, 8, 7
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OFFSET
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1,2
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COMMENTS
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Also known as the 14th Bendersky constant.
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LINKS
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FORMULA
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A(k) = exp(H(k)*B(k+1)/(k+1) - zeta'(-k)), where B(k) is the k-th Bernoulli number, H(k) the k-th Harmonic number, and zeta'(x) is the derivative of the Riemann zeta function.
A(14) = exp(-zeta'(-14)) = exp((B(14)/4)*(zeta(15)/zeta(14))).
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EXAMPLE
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1.338644754241536299558046958873255142542092537062742480234...
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MATHEMATICA
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Exp[N[(BernoulliB[14]/4)*(Zeta[15]/Zeta[14]), 200]]
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CROSSREFS
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Cf. A019727 (A(0)), A074962 (A(1)), A243262 (A(2)), A243263 (A(3)), A243264 (A(4)), A243265 (A(5)), A266553 (A(6)), A266554 (A(7)), A266555 (A(8)), A266556 (A(9)), A266557 (A(10)), A266558 (A(11)), A266559 (A(12)), A260662 (A(13)), A266562 (A(15)), A266563 (A(16)), A266564 (A(17)), A266565 (A(18)), A266566 (A(19)), A266567 (A(20)).
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KEYWORD
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AUTHOR
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STATUS
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approved
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