OFFSET
0,1
COMMENTS
The expression generating this constant is a first degree Eulerian polynomial, in the "variable" e, with coefficient {1}, generated from sum_{n>=0} n^m/e^n, with m=1. See A008292. It approximates m!. - Richard R. Forberg, Feb 15 2015
See A255169 for the second degree polynomial and value.
FORMULA
Equals exp(1)/(exp(1)-1)^2.
From Gleb Koloskov, Jul 12 2021: (Start)
Equals (1/2)/(cosh(1)-1).
EXAMPLE
0.9206735942077923189454135227164996028816556266505511523539604097220...
MAPLE
g:=x->sum(n/exp(n), n=1..x); evalf[110](g(1500)); evalf[110](g(4000));
MATHEMATICA
RealDigits[E/(E-1)^2, 10, 105][[1]] (* Jean-François Alcover, Jan 28 2014 *)
PROG
(PARI) 1+sumalt(n=1, bernreal(2*n)*(1-2*n)/(2*n)!) \\ Gleb Koloskov, Jul 12 2021
CROSSREFS
KEYWORD
cons,nonn
AUTHOR
Joseph Biberstine (jrbibers(AT)indiana.edu), Nov 03 2004
STATUS
approved