A098875 Decimal expansion of Sum_{n>0} n/exp(n).

9, 2, 0, 6, 7, 3, 5, 9, 4, 2, 0, 7, 7, 9, 2, 3, 1, 8, 9, 4, 5, 4, 1, 3, 5, 2, 2, 7, 1, 6, 4, 9, 9, 6, 0, 2, 8, 8, 1, 6, 5, 5, 6, 2, 6, 6, 5, 0, 5, 5, 1, 1, 5, 2, 3, 5, 3, 9, 6, 0, 4, 0, 9, 7, 2, 2, 0, 4, 7, 1, 9, 7, 4, 6, 5, 0, 2, 4, 4, 5, 6, 8, 6, 7, 3, 6, 9, 9, 7, 3, 2, 8, 3, 4, 3, 4, 7, 9, 4, 7, 2, 5, 3, 9, 7

Offset: 0

Author

Joseph Biberstine (jrbibers(AT)indiana.edu), Nov 03 2004

Keywords

• cons
• nonn

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.

Examples

			0.9206735942077923189454135227164996028816556266505511523539604097220...
		

Crossrefs

Cf. A001113, A008292, A010050, A027641, A027642, A073333, A165747, A255169.

Programs

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 *)

PARI

1+sumalt(n=1,bernreal(2*n)*(1-2*n)/(2*n)!) \\ Gleb Koloskov, Jul 12 2021

Formula

Equals exp(1)/(exp(1)-1)^2.

From Gleb Koloskov, Jul 12 2021: (Start)

Equals (1/2)/(cosh(1)-1).

Equals 1+Sum_{n>0} B(2*n)*(1-2*n)/(2*n)! = 1+Sum_{n>0} (A027641(2*n)/A027642(2*n))*A165747(n)/A010050(n).

Equals LambertW(x)*LambertW(-1,x), where x = (1/(1-e))*exp(1/(1-e)) = -A073333*exp(-A073333). (End)