%I #16 Sep 08 2022 08:46:08
%S 2,9,5,3,8,8,6,6,3,9,3,3,0,7,1,6,9,5,8,8,7,1,4,4,9,9,8,3,2,9,5,4,4,1,
%T 5,3,0,9,4,2,7,7,2,4,7,5,1,1,7,7,3,6,3,5,1,5,1,3,7,5,5,5,2,0,4,3,6,6,
%U 3,5,4,4,1,7,8,6,2,0,3,6,0,8,4,8,2,0,7,0,5,0,5,3,9,5,5,7,0,1,2,3,1,3,3,9
%N Decimal expansion of the limit when n -> infinity of the product Product_{k=1..2n+1} (1 - 2/(2*k+1))^(k*(-1)^k).
%H G. C. Greubel, <a href="/A241995/b241995.txt">Table of n, a(n) for n = 1..10000</a>
%H J.-P. Allouche, <a href="http://arxiv.org/abs/1305.6247">A note on products involving zeta(3) and Catalan's constant.</a> arXiv:1305.6247v3 [math.NT], 2013-2014.
%F Equals exp(2*G/Pi + 1/2), where G is Catalan's constant (G = A006752 = 0.915965594...).
%e 2.95388663933071695887144998329544153094277247511773635151375552...
%t RealDigits[Exp[2*Catalan/Pi + 1/2] , 10, 104] // First
%o (PARI) default(realprecision, 100); exp(2*Catalan/Pi + 1/2) \\ _G. C. Greubel_, Aug 25 2018
%o (Magma) SetDefaultRealField(RealField(100)); R:=RealField(); Exp(2*Catalan(R)/Pi(R) + 1/2); // _G. C. Greubel_, Aug 25 2018
%Y Cf. A006752, A241992, A241993, A241994.
%K nonn,cons,easy
%O 1,1
%A _Jean-François Alcover_, Aug 11 2014