OFFSET
0,1
LINKS
István Mező, Problem 11806, Problems and Solutions, The American Mathematical Monthly, Vol. 121, No. 10 (2014), p. 947; Parseval and Kummer, Solution to Problem 11806 by Omran Kouba, ibid., Vol. 123, No. 9 (2016), pp. 943-944.
FORMULA
Equal to log(exp(1/2*log(2*exp(1/3*log(3*exp(1/4*log(4*exp(...)))))))).
Equals log(A296301). - Vaclav Kotesovec, Jun 22 2023
Equals Integral_{x=0..2*Pi} log(Gamma(x/(2*Pi))) * exp(cos(x)) * sin(x + sin(x)) dx - (e-1)*(log(2*Pi)+gamma), where gamma is Euler's constant (A001620) (Mező, 2014). - Amiram Eldar, Jan 25 2024
Equals Integral_{x=0..1} (exp(x) - 1)/(x*log(x)) - (exp(1) - 1)/log(x) dx. - Velin Yanev, Nov 29 2024
EXAMPLE
0.6037828627914879884...
MATHEMATICA
NSum[Log[n]/n!, {n, 2, Infinity}, WorkingPrecision -> 110,
NSumTerms -> 100] // RealDigits[#, 10, 100] &
PROG
(PARI) suminf(n=2, log(n)/n!) \\ Michel Marcus, Jan 31 2019
CROSSREFS
KEYWORD
nonn,cons
AUTHOR
Rok Cestnik, Jan 31 2019
STATUS
approved