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A093720 Decimal expansion of Sum_{n >= 2} zeta(n)/n!.

%I A093720 #28 Feb 16 2025 08:32:53
%S A093720 1,0,7,8,1,8,8,7,2,9,5,7,5,8,1,8,4,8,2,7,5,8,2,6,5,4,3,6,7,6,9,8,3,2,
%T A093720 3,8,1,7,0,7,2,1,9,6,0,9,6,7,2,3,4,7,1,6,0,0,3,7,1,7,0,2,0,7,8,0,0,7,
%U A093720 1,5,2,3,0,0,3,2,7,8,4,3,4,8,6,5,6,7,6,7,6,8,0,8,8,5,8,2,9,0,1
%N A093720 Decimal expansion of Sum_{n >= 2} zeta(n)/n!.
%H A093720 G. C. Greubel, <a href="/A093720/b093720.txt">Table of n, a(n) for n = 1..10000</a>
%H A093720 J. Sondow and E. W. Weisstein, <a href="https://mathworld.wolfram.com/RiemannZetaFunction.html">MathWorld: Riemann Zeta Function</a>
%F A093720 Equals Sum_{k>=1} (exp(1/k) - 1 - 1/k). - _Vaclav Kotesovec_, Mar 04 2016
%F A093720 Equals Integral_{x=0..oo} exp(1/(x^2 + 1))*sin(x/(x^2 + 1))*(coth(Pi*x) - 1) dx + A091725 - 2*A001620 - exp(1)/2 + 3/2. - _Velin Yanev_, Nov 14 2024
%e A093720 1.078188729575818482758265436769832381707219...
%p A093720 evalf(Sum(exp(1/n)-1-1/n, n=1..infinity), 120); # _Vaclav Kotesovec_, Mar 04 2016
%t A093720 digits = 99; ClearAll[z, rd]; z[k_] := z[k] = z[k-1] + N[Sum[Zeta[n]/n!, {n, 2^(k-1) + 1, 2^k}], digits]; z[0] = 0; rd[k_] := rd[k] = RealDigits[z[k]][[1]]; rd[0]; rd[k = 1]; While[ rd[k] != rd[k-1], k++]; rd[k] (* _Jean-François Alcover_, Nov 09 2012 *)
%o A093720 (PARI) suminf(n=2, zeta(n)/n!) \\ _Michel Marcus_, Mar 15 2017
%Y A093720 Cf. A076813, A093721, A269574, A269611, A269720, A269768.
%K A093720 nonn,cons
%O A093720 1,3
%A A093720 _Eric W. Weisstein_, Apr 12 2004
%E A093720 Corrected by _Fredrik Johansson_, Mar 19 2006