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A258086
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Decimal expansion of Integral_{0..infinity} exp(-x)/(1-x*exp(-x)) dx.
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1
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1, 3, 5, 9, 0, 9, 8, 2, 7, 7, 1, 1, 3, 5, 4, 8, 2, 6, 4, 6, 4, 3, 5, 2, 4, 2, 0, 6, 0, 7, 5, 7, 2, 0, 7, 8, 7, 1, 1, 2, 8, 2, 8, 4, 5, 1, 0, 5, 1, 5, 6, 8, 6, 9, 4, 0, 6, 0, 6, 5, 2, 6, 3, 1, 6, 6, 5, 0, 1, 6, 5, 6, 7, 1, 3, 6, 5, 3, 4, 2, 1, 3, 0, 3, 2, 9, 0, 7, 6, 2, 6, 4, 7, 0, 9, 8, 5, 5, 3, 8, 3, 1, 2
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OFFSET
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1,2
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LINKS
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FORMULA
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c = Sum_{i >= 0} i!/(i+1)^(i+1).
Equals Integral_{-exp(-1)..0} (LambertW(x)-LambertW(-1,x))/(1+x)^2 dx. - Gleb Koloskov, Jun 12 2021
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EXAMPLE
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1.35909827711354826464352420607572078711282845105156869406...
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MAPLE
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evalf(Int(exp(-x)/(1-x*exp(-x)), x=0..infinity), 120); # Vaclav Kotesovec, May 19 2015
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MATHEMATICA
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c = NIntegrate[Exp[-x]/(1-x*Exp[-x]), {x, 0, Infinity}, WorkingPrecision -> 103]; RealDigits[c] // First
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PROG
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(PARI) default(realprecision, 120); sumpos(k=0, k!/(k+1)^(k+1)) \\ Vaclav Kotesovec, May 19 2015
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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