%I #10 Sep 08 2022 08:46:08
%S 2,9,2,4,2,7,9,9,9,9,4,4,9,2,1,8,1,5,3,6,0,1,4,5,8,5,4,4,0,2,0,5,7,4,
%T 3,0,0,1,0,6,1,5,2,0,7,0,9,6,8,9,1,5,4,4,4,5,5,5,9,0,0,0,9,7,6,4,7,0,
%U 3,0,6,8,6,8,0,3,0,8,4,3,7,9,2,9,6,3,6,8,6,9,7,4,4,1,3,2,4,4,1,9,7,6,3
%N Decimal expansion of d_0, the constant term in the asymptotic expansion of the average number of registers needed to evaluate a binary tree.
%D Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, Section 5.6 Otter's Tree Enumeration Constants, p. 311.
%H G. C. Greubel, <a href="/A245253/b245253.txt">Table of n, a(n) for n = 0..10000</a>
%H Helmut Prodinger, <a href="http://algo.inria.fr/pfac/PFAC/Program_files/Prodinger.pdf">Philippe Flajolet and the Register function</a>
%H Helmut Prodinger, <a href="http://www.stat.purdue.edu/~mdw/ChapterIntroductions/RegisterFunctionProdinger.pdf">Introduction to Philippe Flajolet’s work on the Register function.</a>
%F d_0 = 1/2 - gamma/(2*log(2)) - 1/log(2) + log(Pi)/log(2), where gamma is Euler's constant (gamma ~ 0.577216).
%e 0.29242799994492181536014585440205743001061520709689154445559...
%t d0 = 1/2 - EulerGamma/(2*Log[2]) - 1/Log[2] + Log[2, Pi]; RealDigits[d0, 10, 103] // First
%o (PARI) default(realprecision, 100); 1/2 - Euler/(2*log(2)) - 1/log(2) + log(Pi)/log(2) \\ _G. C. Greubel_, Sep 06 2018
%o (Magma) SetDefaultRealField(RealField(100)); R:= RealField(); 1/2 - EulerGamma(R)/(2*Log(2)) - 1/Log(2) + Log(Pi(R))/Log(2); // _G. C. Greubel_, Sep 06 2018
%Y Cf. A001620.
%K nonn,cons,easy
%O 0,1
%A _Jean-François Alcover_, Jul 15 2014