|
%I #18 May 17 2018 05:34:51
%S 1,-2,4,-4,2,2,-8,12,-12,6,8,-24,36,-36,16,20,-62,92,-88,40,46,-144,
%T 208,-196,88,102,-308,440,-412,180,208,-624,884,-816,356,404,-1206,
%U 1692,-1552,672,760,-2244,3128,-2852,1224,1378,-4048,5612,-5084,2174,2428,-7104,9796,-8836,3760
%N Expansion of r(q)^2 / r(q^2) in powers of q where r() is the Rogers-Ramanujan continued fraction.
%C Let k(q) = r(q) * r(q^2)^2.
%C G.f. satisfies: A(q) = (1 - k(q))/(1 + k(q)).
%C And r(q)^5 = k(q) * A(q)^2.
%H Seiichi Manyama, <a href="/A285349/b285349.txt">Table of n, a(n) for n = 0..10000</a>
%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Rogers%E2%80%93Ramanujan_continued_fraction">Rogers-Ramanujan continued fraction</a>
%F a(n) = A138518(n) + A285348(n) for n>0 (conjectured). - _Thomas Baruchel_, May 14 2018
%Y r(q)^k / r(q^k): this sequence (k=2), A285628 (k=3), A285629 (k=4), A285630 (k=5).
%Y Cf. A007325, A078905 (r(q)^5), A112274 (k(q)), A285348.
%K sign
%O 0,2
%A _Seiichi Manyama_, Apr 17 2017
|
