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Decimal expansion of the limit when n -> infinity of the product Product_{k=1..2n+1} e^(-1/4)*(1 - 1/(k+1))^((1/2)*k*(k+1)*(-1)^k).
3

%I #11 Jan 03 2021 14:13:36

%S 1,5,8,9,0,5,4,5,2,2,4,7,1,6,6,0,6,3,3,4,8,1,8,1,2,3,5,8,8,6,1,6,6,1,

%T 4,0,8,0,7,9,2,3,5,8,4,4,9,3,2,3,7,7,5,3,3,3,8,3,1,0,1,7,2,3,3,5,5,7,

%U 8,2,3,5,9,4,7,5,2,2,4,1,0,2,2,5,7,4,8,9,3,1,7,5,9,2,2,5,5,0,5,7,5,8,6,6,9

%N Decimal expansion of the limit when n -> infinity of the product Product_{k=1..2n+1} e^(-1/4)*(1 - 1/(k+1))^((1/2)*k*(k+1)*(-1)^k).

%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]

%F exp(7*zeta(3)/(4*Pi^2) + 1/4).

%e 1.5890545224716606334818123588616614080792358449323775333831...

%t RealDigits[Exp[7*Zeta[3]/(4*Pi^2) + 1/4] , 10, 105] // First

%Y Cf. A002117.

%K nonn,cons,easy

%O 1,2

%A _Jean-François Alcover_, Aug 11 2014