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%I #18 Jul 30 2017 10:21:54
%S 1,27,324,2430,13716,64557,265356,983556,3353076,10670373,32031288,
%T 91455804,249948828,657261999,1669898592,4113612864,9853898292,
%U 23010586596,52494114852,117209543940,256559365656,551320914321,1164556135440,2420715030912,4956677613180
%N Expansion of (a(q) / b(q))^3 in powers of q where a(), b() are cubic AGM theta functions.
%C Cubic AGM theta functions: a(q) (see A004016), b(q) (A005928), c(q) (A005882).
%H Seiichi Manyama, <a href="/A290405/b290405.txt">Table of n, a(n) for n = 0..10000</a>
%H J. M. Borwein, P. B. Borwein and F. Garvan, <a href="http://dx.doi.org/10.1090/S0002-9947-1994-1243610-6">Some Cubic Modular Identities of Ramanujan</a>, Trans. Amer. Math. Soc. 343 (1994), 35-47.
%F a(n) = 27 * A121590(n) for n > 0.
%F 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 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 Cf. A000726, A005882, A005928, A121590, A215690.
%K nonn
%O 0,2
%A _Seiichi Manyama_, Jul 30 2017
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