cp's OEIS Frontend

A355499 Decimal expansion of Product_{k>=1} (k - 2/3)^(1/(k - 2/3)) / k^(1/k).

%I A355499 #14 Jul 05 2022 01:49:52
%S A355499 0,4,1,3,0,6,2,4,1,2,5,5,9,3,3,6,3,9,5,2,8,3,8,2,5,2,1,0,0,0,6,7,2,8,
%T A355499 1,0,8,3,1,7,7,4,1,2,9,6,7,4,4,8,6,8,8,5,5,7,7,9,5,4,4,4,0,5,4,6,3,3,
%U A355499 1,9,0,9,5,4,6,4,5,4,5,6,0,0,2,3,1,7,2,6,3,7,3,9,6,5,6,1,7,0,1,9,9,7,0,0,7,2
%N A355499 Decimal expansion of Product_{k>=1} (k - 2/3)^(1/(k - 2/3)) / k^(1/k).
%H A355499 R. W. Gosper, <a href="http://www.tweedledum.com/rwg/idents.htm">Some identities</a>, (d162).
%F A355499 Equals (3^(1/4) * exp(-gamma/2) * Gamma(1/3)^3 / (4*Pi^2))^(Pi/sqrt(3)) / 3^(3*(log(3) + 2*gamma)/4), where gamma is the Euler-Mascheroni constant A001620 and Gamma() is the Gamma function.
%e A355499 0.0413062412559336395283825210006728108317741296744868855779544405463319...
%p A355499 evalf((3^(1/4) * exp(-gamma/2) * GAMMA(1/3)^3 / (4*Pi^2))^(Pi/sqrt(3)) / 3^(3*(log(3) + 2*gamma)/4), 120);
%t A355499 Join[{0},RealDigits[(3^(1/4) * Exp[-EulerGamma/2] * Gamma[1/3]^3/4/Pi^2)^ (Pi/Sqrt[3])/3^(3*(Log[3] + 2*EulerGamma)/4), 10, 120][[1]]]
%o A355499 (PARI) default(realprecision, 200); exp(sumpos(n=1, log(n - 2/3)/(n - 2/3) - log(n)/n))
%Y A355499 Cf. A001620, A115522, A355500.
%K A355499 nonn,cons
%O A355499 0,2
%A A355499 _Vaclav Kotesovec_, Jul 04 2022