A249673 Decimal expansion of Product_{n>=1} cosh(1/n).

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, 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, 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

Offset

1,1

Links

Table of n, a(n) for n=1..105.

Formula

From Amiram Eldar, Jul 30 2023: (Start)

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.

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

Example

2.116465536505484775878572227025831988148089392809082568281348...

Maple

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

Prog

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

Crossrefs

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

Cf. A027641, A027642.

Sequence in context: A327816 A047920 A350269 * A144655 A190782 A369288

Adjacent sequences: A249670 A249671 A249672 * A249674 A249675 A249676

Keyword

nonn,cons

Author

Vaclav Kotesovec, Nov 03 2014

Status

approved