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A266564
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Decimal expansion of the generalized Glaisher-Kinkelin constant A(17).
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20
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1, 5, 9, 6, 5, 3, 5, 0, 8, 5, 7, 5, 8, 0, 3, 8, 5, 5, 3, 8, 5, 1, 4, 5, 5, 2, 3, 6, 6, 2, 0, 4, 4, 1, 9, 4, 5, 3, 3, 1, 6, 6, 1, 1, 0, 0, 6, 1, 3, 5, 0, 4, 4, 4, 3, 4, 1, 4, 5, 5, 4, 6, 3, 9, 9, 9, 7, 1, 1, 0, 6, 0, 4, 5, 3, 4, 3, 2, 2, 9, 5, 6, 3, 5, 0, 6, 5, 4, 0, 4, 2, 1, 1
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OFFSET
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4,2
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COMMENTS
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Also known as the 17th 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(17) = exp(H(17)*B(18)/18 - zeta'(-17)) = exp((B(18)/18)*(EulerGamma + log(2*Pi) - (zeta'(18)/zeta(18))).
Equals (2*Pi*exp(gamma) * Product_{p prime} p^(1/(p^18-1)))^c, where gamma is Euler's constant (A001620), and c = Bernoulli(18)/18 = 43867/14364 (Van Gorder, 2012). - Amiram Eldar, Feb 08 2024
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EXAMPLE
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1596.53508575803855385145523662044194533166110061350444341....
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MATHEMATICA
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Exp[N[(BernoulliB[18]/18)*(EulerGamma + Log[2*Pi] - Zeta'[18]/Zeta[18]), 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)), A266560 (A(14)), A266562 (A(15)), A266563 (A(16)), 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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