A333938 Decimal expansion of Product_{k>=1} (1 - k/2^k).
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, 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, 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
Offset: 0
Examples
0.0788983500212491810064185920122947774736728143458491250873967214687...
Programs
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Maple
evalf(Product(1 - k/2^k, k = 1..infinity), 100);
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Mathematica
Join[{0},RealDigits[Product[1-n/2^n,{n,500}],10,120][[1]]] (* Harvey P. Dale, Jan 12 2024 *) -
PARI
prodinf(k=1, 1 - k/2^k)
Formula
Equals exp(-Sum_{j>=1} polylog(-j, 1/2^j)/j).