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%I #16 Nov 08 2017 02:29:54
%S 1,3,8,4,7,5,3,2,4,2,5,8,4,8,0,4,9,0,4,1,4,3,3,3,3,6,8,5,5,3,5,1,6,2,
%T 8,7,5,8,9,2,9,0,0,0,0,2,1,9,5,7,7,8,3,1,5,8,3,4,3,7,0,8,5,7,1,9,9,4,
%U 3,9,0,8,2,6,3,2,6,6,3,9,8,3,5,4,9,8,9,3,7,0,0,6,8,2,8,5,6,3,9,1
%N Decimal expansion of Integral_(x=1..c) (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="/A240242/b240242.txt">Table of n, a(n) for n = 0..5000</a>
%H Jean-François Alcover, <a href="/A240242/a240242.gif">Graphics</a>
%F A195055 = A013661 + A240242 + A240243.
%F (log(c)/(1+c))^2 = (LambertW(1/e))^2 = 0.0775425...
%e 0.13847532425848...
%t w = ProductLog[1/E]; Pi^2/6 - w - w^2 - 2*Log[1+w]*(1+w) + 2*PolyLog[2, -w] // RealDigits[#, 10, 100]& // First
%o (PARI) (w -> Pi^2/6 - w - w^2 - 2*(1+w)*log(1+w) + 2*polylog(2, -w))(lambertw(exp(-1))) \\ _Charles R Greathouse IV_, Aug 27 2014
%Y Cf. A013661, A141251, A195055, A240243.
%K nonn,cons
%O 0,2
%A _Jean-François Alcover_, Apr 03 2014