(Translated by https://www.hiragana.jp/)
# Greetings from The On-Line Encyclopedia of Integer Sequences! http://oeis.org/ Search: id:a290405 Showing 1-1 of 1 %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 # Content is available under The OEIS End-User License Agreement: http://oeis.org/LICENSE