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A290405 Expansion of (a(q) / b(q))^3 in powers of q where a(), b() are cubic AGM theta functions. 1
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Cubic AGM theta functions: a(q) (see A004016), b(q) (A005928), c(q) (A005882).

LINKS

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.

FORMULA

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.

MATHEMATICA

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 *)

CROSSREFS

Cf. A000726, A005882, A005928, A121590, A215690.

Sequence in context: A224375 A010832 A022719 * A048709 A268973 A160223

Adjacent sequences:  A290402 A290403 A290404 * A290406 A290407 A290408

KEYWORD

nonn

AUTHOR

Seiichi Manyama, Jul 30 2017

STATUS

approved

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Last modified July 3 06:54 EDT 2022. Contains 355031 sequences. (Running on oeis4.)