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%I #21 Jul 30 2023 02:26:40
%S 1,3,0,7,9,7,0,9,3,6,6,6,4,2,8,3,6,4,9,0,1,2,1,0,4,4,7,6,0,0,7,0,5,6,
%T 3,2,0,4,6,5,5,1,5,6,8,3,1,3,8,2,2,3,5,0,6,7,0,5,6,4,8,2,2,5,9,7,9,2,
%U 2,9,3,0,9,8,0,0,9,9,5,4,3,6,4,3,2,1,9,2,2,8,4,8,3,5,9,9,9,0,4,7,0,1,3,7,6
%N Decimal expansion of Product_{k>=1} k*sinh(1/k).
%F Equals exp(Sum_{k>=1} 2^(2*k-1)*B(2*k)*zeta(2*k)/(k*(2*k)!)), where B(k) is the k-th Bernoulli number.
%F Equals exp(Sum_{k>=1} (-1)^(k+1)*zeta(2*k)^2/(k*Pi^(2*k))).
%e 1.30797093666428364901210447600705632046551568313822...
%p evalf(exp(sum(log(k*sinh(1/k)), k = 1 .. infinity)), 120)
%t Block[{$MaxExtraPrecision = 1000}, RealDigits[Exp[Sum[(-1)^(k + 1) * Zeta[2*k]^2 / (k*Pi^(2*k)), {k, 1, 200}]], 10, 120][[1]]]
%o (PARI) exp(-sumpos(k=1,-log(k*sinh(1/k))))
%Y Similar constants: A118817, A249673, A295219.
%Y Cf. A027641, A027642.
%K nonn,cons
%O 1,2
%A _Amiram Eldar_, Jul 30 2023
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