A363502 Decimal expansion of Product_{k>=1} k*sinh(1/k).

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, 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, 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

Offset

1,2

Links

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

Formula

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.

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

Example

1.30797093666428364901210447600705632046551568313822...

Maple

evalf(exp(sum(log(k*sinh(1/k)), k = 1 .. infinity)), 120);

Mathematica

Block[{$MaxExtraPrecision = 1000}, RealDigits[Exp[Sum[(-1)^(k + 1) * Zeta[2*k]^2 / (k*Pi^(2*k)), {k, 1, 200}]], 10, 120][[1]]]

Prog

(PARI) exp(-sumpos(k=1, -log(k*sinh(1/k))))

Crossrefs

Similar constants: A118817, A249673, A295219.

Cf. A027641, A027642.

Sequence in context: A389668 A239022 A343612 * A198488 A296364 A071296

Adjacent sequences: A363499 A363500 A363501 * A363503 A363504 A363505

Keyword

nonn,cons

Author

Amiram Eldar, Jul 30 2023

Status

approved