A249673 - OEIS

%I #17 Jul 30 2023 02:25:02

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

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

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

%N Decimal expansion of Product_{n>=1} cosh(1/n).

%F From _Amiram Eldar_, Jul 30 2023: (Start)

%F Equals exp(Sum_{k>=1} 2^(2*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)*(2^(2*k)-1)*zeta(2*k)^2/(k*Pi^(2*k))). (End)

%e 2.116465536505484775878572227025831988148089392809082568281348...

%p evalf(exp(sum(log(cosh(1/n)), n=1..infinity)), 100)

%o (PARI) default(realprecision,120); exp(sumpos(k=1, log(cosh(1/k))))

%Y Cf. A118817, A230821, A051762, A218504, A246945, A270614.

%Y Cf. A027641, A027642.

%K nonn,cons

%O 1,1

%A _Vaclav Kotesovec_, Nov 03 2014