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%I A290405 #18 Jul 30 2017 10:21:54
%S A290405 1,27,324,2430,13716,64557,265356,983556,3353076,10670373,32031288,
%T A290405 91455804,249948828,657261999,1669898592,4113612864,9853898292,
%U A290405 23010586596,52494114852,117209543940,256559365656,551320914321,1164556135440,2420715030912,4956677613180
%N A290405 Expansion of (a(q) / b(q))^3 in powers of q where a(), b() are cubic AGM theta functions.
%C A290405 Cubic AGM theta functions: a(q) (see A004016), b(q) (A005928), c(q) (A005882).
%H A290405 Seiichi Manyama, Table of n, a(n) for n = 0..10000
%H A290405 J. M. Borwein, P. B. Borwein and F. Garvan, Some Cubic Modular Identities of Ramanujan, Trans. Amer. Math. Soc. 343 (1994), 35-47.
%F A290405 a(n) = 27 * A121590(n) for n > 0.
%F A290405 G.f.: (1 + 9*(eta(q^9)/eta(q))^3)^3 = 1 + 27*(eta(q^3)/eta(q))^12 = 1 + (c(q) / b(q))^3.
%t A290405 nmax = 20; CoefficientList[Series[1 + 27*x*Product[(1 + x^k + x^(2*k))^12, {k, 1, nmax}], {x, 0, nmax}], x] (* _Vaclav Kotesovec_, Jul 30 2017 *)
%Y A290405 Cf. A000726, A005882, A005928, A121590, A215690.
%K A290405 nonn
%O A290405 0,2
%A A290405 _Seiichi Manyama_, Jul 30 2017
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