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%I #10 Nov 09 2017 05:05:49
%S 1,5,0,6,4,5,8,7,4,2,5,8,9,7,4,5,9,4,6,0,5,8,0,8,1,7,9,8,0,9,2,5,0,8,
%T 9,0,1,6,2,9,6,5,9,9,0,0,9,8,7,2,2,0,6,0,6,1,5,2,1,2,1,1,4,3,6,5,0,0,
%U 6,3,5,6,2,1,3,9,9,3,4,4,7,5,4,7,8,6,3,9,5,3,0,5,5,1,4,7,3,0,6,6
%N Decimal expansion of Integral_(x=c..infinity) (log(x)/(1+x))^2 dx, where c = A141251 = e^(LambertW(1/e)+1) corresponds to the maximum of the function.
%H G. C. Greubel, <a href="/A240243/b240243.txt">Table of n, a(n) for n = 1..5000</a>
%F A195055 = A013661 + A240242 + A240243.
%e 1.50645874258974594605808179809250890162965990098722060615212114365006356...
%t w = ProductLog[1/E]; w + w^2 + 2 *Log[1+w]*(1+w) - 2*PolyLog[2, -w] // RealDigits[#, 10, 100]& // First
%o (PARI) (w -> w + w^2 + 2*(1+w)*log(1+w) - 2*polylog(2, -w))(lambertw(exp(-1)))
%Y Cf. A013661, A141251, A195055, A240242.
%K nonn,cons
%O 1,2
%A _Jean-François Alcover_, Apr 03 2014