A355500 Decimal expansion of Product_{k>=1} (k - 1/2)^(1/(k - 1/2)) / k^(1/k).
2, 7, 7, 8, 5, 8, 3, 4, 7, 8, 3, 2, 7, 2, 3, 8, 7, 8, 4, 9, 0, 7, 0, 8, 5, 2, 3, 3, 3, 0, 3, 0, 9, 7, 3, 2, 9, 9, 7, 3, 3, 7, 2, 6, 4, 4, 7, 0, 3, 2, 6, 5, 0, 8, 0, 6, 4, 6, 3, 1, 1, 8, 0, 5, 8, 6, 7, 7, 6, 3, 7, 9, 6, 4, 5, 4, 6, 9, 3, 2, 3, 1, 9, 8, 6, 5, 9, 4, 8, 9, 4, 4, 6, 8, 6, 1, 6, 4, 1, 7, 6, 5, 3, 3, 1, 1
Offset: 0
Examples
0.277858347832723878490708523330309732997337264470326508064631180586776...
Programs
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Maple
evalf(1 / 2^(2*gamma + log(2)), 120);
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Mathematica
RealDigits[1 / 2^(2*EulerGamma + Log[2]), 10, 120][[1]]
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PARI
default(realprecision, 200); exp(sumpos(n=1, log(n - 1/2)/(n - 1/2) - log(n)/n))
Formula
Equals 1 / 2^(2*gamma + log(2)), where gamma is the Euler-Mascheroni constant A001620.