A295219 Decimal expansion of Product_{n>=1} n*sin(1/n).

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

Offset

0,1

Links

Table of n, a(n) for n=0..87.

Formula

Equals 1*sin(1/1) * 2*sin(1/2) * 3*sin(1/3) * 4*sin(1/4) * 5*sin(1/5) * ...

From Amiram Eldar, Jul 30 2023: (Start)

Equals exp(Sum_{k>=1} 2^(2*k-1)*(-1)^k*B(2*k)*zeta(2*k)/(k*(2*k)!)), where B(k) is the k-th Bernoulli number.

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

Example

0.75536338851857321406336498617047655...

Maple

evalf(Product(n*sin(1/n), n = 1..infinity), 120); # Vaclav Kotesovec, Jun 23 2021

Prog

(PARI)
  \\ Set the precision at least twice than the
  \\ number of desired correct decimal digits
  default(realprecision, 200);  \\ To get the first 100 digits right
  exp(-sumpos(n=1, -log(n*sin(1/n))))

Crossrefs

Cf. A118817.

Cf. A027641, A027642.

Sequence in context: A258042 A340710 A289003 * A138313 A138312 A152115

Adjacent sequences: A295216 A295217 A295218 * A295220 A295221 A295222

Keyword

nonn,cons

Author

Michal Paulovic, Nov 17 2017

Extensions

Terms corrected by Jinyuan Wang, Jul 21 2020

Status

approved