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A363502
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Decimal expansion of Product_{k>=1} k*sinh(1/k).
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0
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1, 3, 0, 7, 9, 7, 0, 9, 3, 6, 6, 6, 4, 2, 8, 3, 6, 4, 9, 0, 1, 2, 1, 0, 4, 4, 7, 6, 0, 0, 7, 0, 5, 6, 3, 2, 0, 4, 6, 5, 5, 1, 5, 6, 8, 3, 1, 3, 8, 2, 2, 3, 5, 0, 6, 7, 0, 5, 6, 4, 8, 2, 2, 5, 9, 7, 9, 2, 2, 9, 3, 0, 9, 8, 0, 0, 9, 9, 5, 4, 3, 6, 4, 3, 2, 1, 9, 2, 2, 8, 4, 8, 3, 5, 9, 9, 9, 0, 4, 7, 0, 1, 3, 7, 6
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OFFSET
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1,2
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LINKS
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FORMULA
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Equals exp(Sum_{k>=1} 2^(2*k-1)*B(2*k)*zeta(2*k)/(k*(2*k)!)), where B(k) is the k-th Bernoulli number.
Equals exp(Sum_{k>=1} (-1)^(k+1)*zeta(2*k)^2/(k*Pi^(2*k))).
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EXAMPLE
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1.30797093666428364901210447600705632046551568313822...
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MAPLE
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evalf(exp(sum(log(k*sinh(1/k)), k = 1 .. infinity)), 120)
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MATHEMATICA
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Block[{$MaxExtraPrecision = 1000}, RealDigits[Exp[Sum[(-1)^(k + 1) * Zeta[2*k]^2 / (k*Pi^(2*k)), {k, 1, 200}]], 10, 120][[1]]]
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PROG
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(PARI) exp(-sumpos(k=1, -log(k*sinh(1/k))))
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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