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A290405
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Expansion of (a(q) / b(q))^3 in powers of q where a(), b() are cubic AGM theta functions.
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1
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1, 27, 324, 2430, 13716, 64557, 265356, 983556, 3353076, 10670373, 32031288, 91455804, 249948828, 657261999, 1669898592, 4113612864, 9853898292, 23010586596, 52494114852, 117209543940, 256559365656, 551320914321, 1164556135440, 2420715030912, 4956677613180
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OFFSET
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0,2
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COMMENTS
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Cubic AGM theta functions: a(q) (see A004016), b(q) (A005928), c(q) (A005882).
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LINKS
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Seiichi Manyama, Table of n, a(n) for n = 0..10000
J. M. Borwein, P. B. Borwein and F. Garvan, Some Cubic Modular Identities of Ramanujan, Trans. Amer. Math. Soc. 343 (1994), 35-47.
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FORMULA
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a(n) = 27 * A121590(n) for n > 0.
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.
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MATHEMATICA
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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 *)
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CROSSREFS
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Cf. A000726, A005882, A005928, A121590, A215690.
Sequence in context: A224375 A010832 A022719 * A048709 A268973 A160223
Adjacent sequences: A290402 A290403 A290404 * A290406 A290407 A290408
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KEYWORD
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nonn
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AUTHOR
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Seiichi Manyama, Jul 30 2017
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STATUS
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approved
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