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 A229837 Decimal expansion of Sum_{n>=1} 1/(n*n!). 5
 1, 3, 1, 7, 9, 0, 2, 1, 5, 1, 4, 5, 4, 4, 0, 3, 8, 9, 4, 8, 6, 0, 0, 0, 8, 8, 4, 4, 2, 4, 9, 2, 3, 1, 8, 3, 7, 9, 7, 4, 9, 0, 1, 2, 4, 5, 7, 9, 2, 7, 8, 3, 9, 9, 2, 8, 4, 0, 4, 6, 1, 1, 9, 6, 9, 9, 7, 6, 4, 6, 1, 0, 7, 7, 5, 6, 1, 3, 9, 4, 8, 2, 6, 1, 1, 9, 5, 3, 6, 4, 6, 8, 3, 4, 3, 9, 2, 2, 0, 7 (list; constant; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 LINKS G. C. Greubel, Table of n, a(n) for n = 1..10000 Stephen Crowley, Two New Zeta Constants, arXiv:1207.1126 [math.NT], 2012, page 17. Wikipedia, Logarithmic integral function. FORMULA Sum_{n >= 1} 1/(n*n!) = Ei(1)-gamma where Ei is the exponential integral and gamma is Euler's constant. Also pFq(1,1; 2,2; 1) where pFq is the generalized hypergeometric function. Also li(e)-gamma, e being the Euler constant (A001113) and li the logarithmic integral function. - Stanislav Sykora, May 09 2015 Continued fraction expansion: Ei(1) - gamma = 1/(1 - 1^3/(5 - 2^3/(11 -...-(n-1)^3/(n^2+n-1) -...))). See A061572. - Peter Bala, Feb 01 2017 From Amiram Eldar, Aug 01 2020: (Start) Equals Sum_{k>=1} H(k)*k/(k+1)!, where H(k) = A001008(k)/A002805(k) is the k-th harmonic number. Equals Integral_{x=0..1} (exp(x) - 1)/x dx. Equals -Integral_{x=0..1} exp(x)*log(x) dx. Equals -Integral_{x=1..e} log(log(x)) dx. (End) Equals e * Sum_{k>=1} (-1)^(k+1)*H(k)/k!, where H(k) = A001008(k)/A002805(k) is the k-th harmonic number. - Amiram Eldar, Jun 25 2021 EXAMPLE 1.3179021514544038948600088442492318379749012457927839928404611969976461... MAPLE evalf(Ei(1)-gamma, 120); # Vaclav Kotesovec, May 10 2015 MATHEMATICA RealDigits[ ExpIntegralEi[1] - EulerGamma, 10, 100] // First PROG (PARI) -Euler-real(eint1(-1)) \\ Charles R Greathouse IV, Oct 01 2013 CROSSREFS Cf. A001008, A001113, A001620, A002805, A091725, A061572, A264806. Sequence in context: A271059 A121370 A137908 * A019639 A306566 A329943 Adjacent sequences:  A229834 A229835 A229836 * A229838 A229839 A229840 KEYWORD nonn,cons,changed AUTHOR Jean-François Alcover, Oct 01 2013 STATUS approved

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Last modified July 30 06:21 EDT 2021. Contains 346348 sequences. (Running on oeis4.)