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Decimal expansion of Product_{k>=1} (1 - k/2^k).
1

%I #9 Jan 12 2024 18:03:03

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

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

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

%N Decimal expansion of Product_{k>=1} (1 - k/2^k).

%F Equals exp(-Sum_{j>=1} polylog(-j, 1/2^j)/j).

%e 0.0788983500212491810064185920122947774736728143458491250873967214687...

%p evalf(Product(1 - k/2^k, k = 1..infinity), 100);

%t Join[{0},RealDigits[Product[1-n/2^n,{n,500}],10,120][[1]]] (* _Harvey P. Dale_, Jan 12 2024 *)

%o (PARI) prodinf(k=1, 1 - k/2^k)

%Y Cf. A048651, A065446, A277355.

%K nonn,cons

%O 0,2

%A _Vaclav Kotesovec_, Apr 11 2020