Search: id:A122858
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%I A122858
%S A122858 1,8,8,32,40,48,32,64,104,104,48,96,160,112,64,192,232,144,104,160,240,
               256,
%T A122858 96,192,416,248,112,320,320,240,192,256,488,384,144,384,520,304,160,448,
               624,
%U A122858 336,256,352,480,624,192,384,928,456,248,576,560,432,320,576,832
%V A122858 1,8,-8,32,-40,48,-32,64,-104,104,-48,96,-160,112,-64,192,-232,144,-104,
               160,-240,256,
%W A122858 -96,192,-416,248,-112,320,-320,240,-192,256,-488,384,-144,384,-520,304,
               -160,448,-624,
%X A122858 336,-256,352,-480,624,-192,384,-928,456,-248,576,-560,432,-320,576,-832
%N A122858 Expansion of E(k)K(k)(2/pi)^2 in powers of q^2 where E(k),K(k) are complete 
               elliptic integrals and q=exp(-pi*K(k')/K(k)).
%F A122858 Expansion of (4P(q^2)-P(q))/3 in powers of q where P() is a Ramanujan 
               Lambert series.
%F A122858 G.f.: 1 +8*Sum_{k>0} x^k/(1+x^k)^2 = 1 -8*Sum_{k>0} k*(-x)^k/(1-x^k) 
               = 1 +8*Sum_{k>0} k*x^k*(1-3*x^k)/(1-x^(2*k)).
%o A122858 (PARI) {a(n)=if(n<1, n==0, -8*sumdiv(n, d, (-1)^d*d))}
%Y A122858 A002129(n)*8=a(n) if n>0.
%Y A122858 Sequence in context: A098360 A133038 A143336 this_sequence A053596 A141384 
               A111218
%Y A122858 Adjacent sequences: A122855 A122856 A122857 this_sequence A122859 A122860 
               A122861
%K A122858 sign
%O A122858 0,2
%A A122858 Michael Somos, Sep 15 2006

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