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%I #13 Jun 12 2021 02:47:49
%S 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,
%T 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,
%U 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
%N Decimal expansion of Integral_{0..infinity} exp(-x)/(1-x*exp(-x)) dx.
%H MathOverflow, <a href="http://mathoverflow.net/questions/206917">Upper bound of the waiting time of a sum process.</a>
%F c = Sum_{i >= 0} i!/(i+1)^(i+1).
%F Equals Integral_{-exp(-1)..0} (LambertW(x)-LambertW(-1,x))/(1+x)^2 dx. - _Gleb Koloskov_, Jun 12 2021
%e 1.35909827711354826464352420607572078711282845105156869406...
%p evalf(Int(exp(-x)/(1-x*exp(-x)),x=0..infinity),120); # _Vaclav Kotesovec_, May 19 2015
%t c = NIntegrate[Exp[-x]/(1-x*Exp[-x]), {x, 0, Infinity}, WorkingPrecision -> 103]; RealDigits[c] // First
%o (PARI) default(realprecision,120); sumpos(k=0, k!/(k+1)^(k+1)) \\ _Vaclav Kotesovec_, May 19 2015
%K nonn,cons,easy
%O 1,2
%A _Jean-François Alcover_, May 19 2015
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