%I A143336
%S A143336 1,8,8,32,40,48,32,64,104,104,48,96,160,112,64,192,232,144,104,160,240,
%T A143336 256,96,192,416,248,112,320,320,240,192,256,488,384,144,384,520,304,160,
%U A143336 448,624,336,256,352,480,624,192,384,928,456,248,576,560,432,320,576
%V A143336 1,-8,-8,-32,-40,-48,-32,-64,-104,-104,-48,-96,-160,-112,-64,-192,-232,
               -144,-104,-160,
%W A143336 -240,-256,-96,-192,-416,-248,-112,-320,-320,-240,-192,-256,-488,-384,
               -144,-384,-520,
%X A143336 -304,-160,-448,-624,-336,-256,-352,-480,-624,-192,-384,-928,-456,-248,
               -576,-560,-432
%N A143336 Expansion of K(k) * (2 * E(k) - K(k)) * (2/pi)^2 in powers of q where 
               E(k), K(k) are complete elliptic integrals and q = exp(-pi * K(k') 
               / K(k)).
%F A143336 The generating function equals 0 when 2 * E(k) = K(k) at q = Lambda = 
               0.1076539192... (A072558) the "One-Ninth" constant.
%F A143336 Expansion of (P(q) - 2 * P(q^2) + 4 * P(q^4))/3 in powers of q where 
               P() is a Ramanujan Lambert series.
%F A143336 G.f.: 1 - 8 * Sum_{k>0} k * x^k / (1 - (-x)^k) = 1 + 8 * Sum_{k>0} (-x)^k 
               / (1 + (-x)^k)^2.
%e A143336 1 - 8*q - 8*q^2 - 32*q^3 - 40*q^4 - 48*q^5 - 32*q^6 - 64*q^7 - 104*q^8 
               + ...
%o A143336 (PARI) {a(n) = if( n<1, n==0, -(-1)^n * 8 * sumdiv(n, d, (-1)^d * d))}
%Y A143336 (-1)^n * A122858(n) = a(n). -8 * A113184(n) = a(n) unless n=0.
%Y A143336 Sequence in context: A077110 A098360 A133038 this_sequence A122858 A053596 
               A141384
%Y A143336 Adjacent sequences: A143333 A143334 A143335 this_sequence A143337 A143338 
               A143339
%K A143336 sign
%O A143336 0,2
%A A143336 Michael Somos, Aug 09 2008