A308666 Decimal expansion of sinh(sqrt(2)*Pi)/(3*sqrt(2)*Pi).

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

Offset: 1

Author

Ilya Gutkovskiy, Jun 15 2019

Keywords

• nonn
• cons
• changed

Examples

			3.188917887548962422285938616665096752406529595142992...
		

Links

• Kelvin Voskuijl, Table of n, a(n) for n = 1..20000

Crossrefs

Cf. A000292, A084248, A308642.

Programs

Mathematica

RealDigits[Sinh[Sqrt[2] Pi]/(3 Sqrt[2] Pi), 10, 120][[1]]
RealDigits[Product[(1 + 1/(k (k + 1) (k + 2)/6)), {k, 1, Infinity}], 10, 120][[1]]

PARI

sinh(sqrt(2)*Pi)/(3*sqrt(2)*Pi) \\ Michel Marcus, Jun 15 2019

Formula

Equals Product_{k>=1} (1 + 1/(k*(k + 1)*(k + 2)/6)).

Equals Product_{k>=1} (1 + 1/A000292(k)).

Equals Product_{k>=2} (1 + 2/k^2). - Amiram Eldar, Aug 02 2020