A308666 - OEIS

%I #11 Aug 02 2020 04:10:29

%S 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,

%T 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,

%U 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

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

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

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

%F Equals Product_{k>=2} (1 + 2/k^2). - _Amiram Eldar_, Aug 02 2020

%e 3.188917887548962422285938616665096752406529595142992...

%t RealDigits[Sinh[Sqrt[2] Pi]/(3 Sqrt[2] Pi), 10, 120][[1]]

%t RealDigits[Product[(1 + 1/(k (k + 1) (k + 2)/6)), {k, 1, Infinity}], 10, 120][[1]]

%o (PARI) sinh(sqrt(2)*Pi)/(3*sqrt(2)*Pi) \\ _Michel Marcus_, Jun 15 2019

%Y Cf. A000292, A084248, A308642.

%K nonn,cons

%O 1,1

%A _Ilya Gutkovskiy_, Jun 15 2019