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A094082 Decimal expansion of Sum_{n>=1} (n!/n^n).

%I A094082 #33 May 10 2023 10:53:07
%S A094082 1,8,7,9,8,5,3,8,6,2,1,7,5,2,5,8,5,3,3,4,8,6,3,0,6,1,4,5,0,7,0,9,6,0,
%T A094082 0,3,8,8,1,9,8,7,3,4,0,0,4,8,9,2,8,9,9,0,4,8,2,9,6,1,7,6,6,9,1,2,2,2,
%U A094082 9,6,3,8,6,6,6,1,2,1,4,2,1,1,3,6,1,7,6,5,0,1,9,7,3,8,9,1,2,3,5,3,2,3,9,6,8
%N A094082 Decimal expansion of Sum_{n>=1} (n!/n^n).
%C A094082 Sum_{n>=1} n!/n^(n+2) = Integral_{x=0..infinity} -log(1-x*exp(-x)) dx = 1.157694752682... . - _Vaclav Kotesovec_, Jan 05 2016
%F A094082 Equals Integral_{x=0..oo} x*exp(x)/(exp(x)-x)^2 dx. - _Michael Somos_, May 18 2021
%F A094082 Equals Integral_{x=1..oo} 1/(x - log(x))^2 dx. - _Fabián Pereyra_, May 10 2023
%e A094082 1.879853862175258533486306145...
%t A094082 RealDigits[ NSum[n!/n^n, {n, 1, Infinity}, WorkingPrecision -> 110, NSumTerms -> 180] , 10, 99] // First (* _Jean-François Alcover_, Feb 12 2013 *)
%t A094082 RealDigits @ NIntegrate[x E^x/(E^x - x)^2, {x, 0, Infinity}, WorkingPrecision -> 105] // First (* _Michael Somos_, May 18 2021 *)
%o A094082 (PARI) firstDecimalDigits(n)={default(realprecision,n);return(digits(floor(suminf(n=1,n!/(n^n))*10^n)))}
%o A094082 print(firstDecimalDigits(98)); \\ _R. J. Cano_, Dec 30 2016
%o A094082 (PARI) suminf(n=1,n!/(n^n)) \\ _Michel Marcus_, Dec 30 2016
%Y A094082 Cf. A055775, A073225.
%K A094082 nonn,cons
%O A094082 1,2
%A A094082 _Ross La Haye_, May 01 2004
%E A094082 More terms from Francisco Salinas (franciscodesalinas(AT)hotmail.com), May 01 2004