A334397 Decimal expansion of (e - 2)/e.

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

Offset: 0

Author

Daniel Hoyt, Apr 26 2020

Keywords

• nonn
• cons

Examples

			0.2642411176571153568089524596770782651...
		

Links

• M. L. Glasser, A note on Beukers's and related integrals, Amer. Math. Monthly 126(4) (2019), 361-363.

Crossrefs

Cf. A001008, A001113, A002805, A019739, A135002, A309419, A334396.

Programs

Mathematica

RealDigits[1 - 2/E, 10, 100][[1]] (* Alonso del Arte, Apr 26 2020 *)

PARI

1 - 2/exp(1) \\ Michel Marcus, May 01 2020

Formula

Equals Integral_{x=0..1} x/e^x dx.

Equals 1 - A135002.

Equals 1/A309419.

Equals -Integral_{x=0..1, y=0..1} x*y/(exp(x*y)*log(x*y)) dx dy. (Apply Theorem 1 or Theorem 2 of Glasser (2019) to the above integral.) - Petros Hadjicostas, Jun 30 2020

From Amiram Eldar, Aug 05 2020: (Start)

Equals Sum_{k>=0} (-1)^k/(k! * (k+2)).

Equals Sum_{k>=1} 1/((2*k)! * (k+1)).

Equals Sum_{k>=1} (-1)^k * k^2 * H(k)/k!, where H(k) = A001008(k)/A002805(k) is the k-th harmonic number. (End)