%I A110625
%S A110625 1,1,3,101,5807,77801,82949,170636,170636,170636,363113,363113,84848,
%T A110625 710567,22435781,3901243741,27210449083,1003538672911,248595095590537,
%U A110625 10165684261926701,438167567023512863,439119040574907047
%N A110625 Numerator of b(n) = -Sum(k=1 to n, A037861(k)/((2k)(2k+1))), where A037861(k) 
               = (number of 0's) - (number of 1's) in binary representation of k.
%C A110625 Numerators of partial sums of a series for log 4/Pi. Denominators are 
               A110626.
%D A110625 J. Sondow, Double integrals for Euler's constant and ln(4/Pi) and an 
               analog of Hadjicostas's formula, Amer. Math. Monthly 112 (2005) 61-65.
%H A110625 J. Sondow, <a href="http://arXiv.org/abs/math.NT/0508042">New Vacca-Type 
               Rational Series for Euler's Constant and Its "Alternating" Analog 
               ln(4/Pi)</a>
%F A110625 lim(n -> infinity, b(n)) = log 4/Pi = 0.24156...
%e A110625 a(3) = 3 because b(3) = 1/6 + 0 + 1/21 = 3/14.
%Y A110625 Cf. A037861, A073099, A094640, A110626.
%Y A110625 Sequence in context: A037114 A069457 A142416 this_sequence A108220 A130733 
               A037062
%Y A110625 Adjacent sequences: A110622 A110623 A110624 this_sequence A110626 A110627 
               A110628
%K A110625 easy,frac,nonn
%O A110625 1,3
%A A110625 Jonathan Sondow (jsondow(AT)alumni.princeton.edu), Aug 01 2005