A094082 Decimal expansion of Sum_{n>=1} (n!/n^n).
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
Offset: 1
Examples
1.879853862175258533486306145...
Programs
-
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 *) -
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
Formula
Equals Integral_{x=0..oo} x*exp(x)/(exp(x)-x)^2 dx. - Michael Somos, May 18 2021
Equals Integral_{x=1..oo} 1/(x - log(x))^2 dx. - Fabián Pereyra, May 10 2023
Extensions
More terms from Francisco Salinas (franciscodesalinas(AT)hotmail.com), May 01 2004
Comments