A272055 - OEIS

%I #10 Sep 07 2018 20:31:08

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

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

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

%N Decimal expansion of -1/(e^2 Ei(-1)), an increasing rooted tree enumeration constant associated with the Euler-Gompertz constant, where Ei is the exponential integral.

%D Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, Section 5.6 Otter's tree enumeration constants, p. 303.

%H G. C. Greubel, <a href="/A272055/b272055.txt">Table of n, a(n) for n = 0..10000</a>

%H F. Bergeron, Ph. Flajolet and B. Salvy, <a href="http://algo.inria.fr/flajolet/Publications/BeFlSa92.pdf">Varieties of Increasing Trees</a>, Lecture Notes in Computer Science vol. 581, ed. J.-C. Raoult, Springer-Verlag, 1992, pp. 24-48.

%H Eric Weisstein's MathWorld, <a href="http://mathworld.wolfram.com/GompertzConstant.html">Gompertz Constant</a>

%H Eric Weisstein's MathWorld, <a href="http://mathworld.wolfram.com/ExponentialIntegral.html">Exponential Integral</a>

%H Eric Weisstein's MathWorld, <a href="http://mathworld.wolfram.com/RootedTree.html">Rooted Tree</a>

%H <a href="/index/Mo#mobiles">Index entries for sequences related to mobiles</a>

%F Equals 1 / (e * A073003).

%F Also equals  -1 / (e^2 * (gamma - Sum_{n>=1} (-1)^(n-1)/(n*n!))), where gamma is the Euler-Mascheroni constant A001620.

%e 0.61688784828072707144493834566228549352490056933168817865661...

%t RealDigits[-1/(E^2*ExpIntegralEi[-1]), 10, 103][[1]]

%o (PARI) default(realprecision, 100); 1/(exp(2)*eint1(1)) \\ _G. C. Greubel_, Sep 07 2018

%Y Cf. A029768, A073003.

%K nonn,cons

%O 0,1

%A _Jean-François Alcover_, Apr 19 2016