OFFSET
0,1
COMMENTS
From Johannes W. Meijer, Jun 27 2016: (Start)
This constant is related to the values of zeta(2*n-1) of the Riemann zeta function and the Euler Mascheroni constant gamma. If we define Z(n) = (1/n) * (sum(zeta(2*n-2*k-1) * Z(k), k=0..n-2) + gamma * Z(n-1)), with Z(0) = 1, then limit(Z(n), n -> infinity) = 2/exp(1).
The structure of the n! * Z(n) formulas leads to the multinomial coefficients A036039. (End).
FORMULA
Integral of log x from x = 1/e to e. - Charles R Greathouse IV, Apr 16 2015
Equals lim_{k->0} 2*(1 - k)^(1/k). - Ilya Gutkovskiy, Jun 27 2016
Equals Sum_{i>=0} ((-1)^i)(1-i)/i!. - Maciej Kaniewski, Sep 10 2017
Equals Sum_{i>=0} ((-1)^i)(i^2+2)/i!. - Maciej Kaniewski, Sep 12 2017
From Peter Bala, Mar 21 2022: (Start)
2/e = Integral_{x = 1..oo} (2*x/(1+x))^n*(x^2+x+1-n)/x^2*exp(-x) dx;
2/e = - Integral_{x = 0..1} (2*x/(1+x))^n*(x^2+x+1-n)/x^2*exp(-x) dx, both valid for n >= 2. (End)
EXAMPLE
0.735758882342... = 2*A068985.
MAPLE
evalf(2/exp(1)) ; # R. J. Mathar, Jul 14 2013
MATHEMATICA
RealDigits[2/E, 10, 120][[1]] (* Harvey P. Dale, Dec 25 2013 *)
PROG
(PARI) 2*exp(-1) \\ Charles R Greathouse IV, Apr 16 2015
CROSSREFS
KEYWORD
nonn,cons
AUTHOR
Omar E. Pol, Nov 15 2007
STATUS
approved