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

%I A334397 #35 Aug 05 2020 09:43:04
%S A334397 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,
%T A334397 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,
%U A334397 7,0,0,8,5,1,0,2,0,0,3,9,3,2,8,5,7,0,5,4,5
%N A334397 Decimal expansion of (e - 2)/e.
%H A334397 M. L. Glasser, <a href="https://doi.org/10.1080/00029890.2019.1565856">A note on Beukers's and related integrals</a>, Amer. Math. Monthly 126(4) (2019), 361-363.
%F A334397 Equals Integral_{x=0..1} x/e^x dx.
%F A334397 Equals 1 - A135002.
%F A334397 Equals 1/A309419.
%F A334397 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
%F A334397 From _Amiram Eldar_, Aug 05 2020: (Start)
%F A334397 Equals Sum_{k>=0} (-1)^k/(k! * (k+2)).
%F A334397 Equals Sum_{k>=1} 1/((2*k)! * (k+1)).
%F A334397 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)
%e A334397 0.2642411176571153568089524596770782651...
%t A334397 RealDigits[1 - 2/E, 10, 100][[1]] (* _Alonso del Arte_, Apr 26 2020 *)
%o A334397 (PARI) 1 - 2/exp(1) \\ _Michel Marcus_, May 01 2020
%Y A334397 Cf. A001008, A001113, A002805, A019739, A135002, A309419, A334396.
%K A334397 nonn,cons
%O A334397 0,1
%A A334397 _Daniel Hoyt_, Apr 26 2020