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A355500 Decimal expansion of Product_{k>=1} (k - 1/2)^(1/(k - 1/2)) / k^(1/k).

%I A355500 #14 Jul 04 2022 19:56:58
%S A355500 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,
%T A355500 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,
%U A355500 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
%N A355500 Decimal expansion of Product_{k>=1} (k - 1/2)^(1/(k - 1/2)) / k^(1/k).
%F A355500 Equals 1 / 2^(2*gamma + log(2)), where gamma is the Euler-Mascheroni constant A001620.
%e A355500 0.277858347832723878490708523330309732997337264470326508064631180586776...
%p A355500 evalf(1 / 2^(2*gamma + log(2)), 120);
%t A355500 RealDigits[1 / 2^(2*EulerGamma + Log[2]), 10, 120][[1]]
%o A355500 (PARI) default(realprecision, 200); exp(sumpos(n=1, log(n - 1/2)/(n - 1/2) - log(n)/n))
%Y A355500 Cf. A001620, A115522, A355499.
%K A355500 nonn,cons
%O A355500 0,1
%A A355500 _Vaclav Kotesovec_, Jul 04 2022