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 A094082 Decimal expansion of Sum_{n>=1} (n!/n^n). 6
 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, 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, 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 (list; constant; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Sum_{n>=1} n!/n^(n+2) = Integral_{x=0..infinity} -log(1-x*exp(-x)) dx = 1.157694752682... . - Vaclav Kotesovec, Jan 05 2016 LINKS FORMULA Equals Integral_{x=0..oo} x*exp(x)/(exp(x)-x)^2 dx. - Michael Somos, May 18 2021 EXAMPLE 1.879853862175258533486306145... MATHEMATICA RealDigits[ NSum[n!/n^n, {n, 1, Infinity}, WorkingPrecision -> 110, NSumTerms -> 180] , 10, 99] // First (* Jean-François Alcover, Feb 12 2013 *) RealDigits @ NIntegrate[x E^x/(E^x - x)^2, {x, 0, Infinity}, WorkingPrecision -> 105] // First (* Michael Somos, May 18 2021 *) PROG (PARI) firstDecimalDigits(n)={default(realprecision, n); return(digits(floor(suminf(n=1, n!/(n^n))*10^n)))} print(firstDecimalDigits(98)); \\ R. J. Cano, Dec 30 2016 (PARI) suminf(n=1, n!/(n^n)) \\ Michel Marcus, Dec 30 2016 CROSSREFS Cf. A055775, A073225. Sequence in context: A199389 A256490 A197688 * A318378 A198884 A212911 Adjacent sequences:  A094079 A094080 A094081 * A094083 A094084 A094085 KEYWORD nonn,cons AUTHOR Ross La Haye, May 01 2004 EXTENSIONS More terms from Francisco Salinas (franciscodesalinas(AT)hotmail.com), May 01 2004 STATUS approved

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Last modified May 24 19:38 EDT 2022. Contains 354043 sequences. (Running on oeis4.)