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

1,2

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

Table of n, a(n) for n=1..105.

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

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