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%I #36 Nov 19 2022 05:41:48
%S 1,0,-1,0,-2,0,0,0,1,0,4,0,-2,0,2,0,2,0,-4,0,0,0,-8,0,-1,0,-1,0,6,0,8,
%T 0,-4,0,0,0,6,0,2,0,-6,0,4,0,-2,0,0,0,-7,0,-2,0,-2,0,-8,0,4,0,4,0,-2,
%U 0,0,0,4,0,-4,0,8,0,8,0,10,0,1,0,0,0,-8,0,1,0
%N Expansion of eta(q^2) * eta(q^4) * eta(q^6) * eta(q^12) in powers of q.
%C The bisection of this sequence containing all nonzero terms is A030188.
%C Multiplicative. See A030188 for formula. - _Andrew Howroyd_, Jul 31 2018
%H Seiichi Manyama, <a href="/A276847/b276847.txt">Table of n, a(n) for n = 1..10000</a>
%H Yves Martin and Ken Ono, <a href="http://dx.doi.org/10.1090/S0002-9939-97-03928-2">Eta-Quotients and Elliptic Curves</a>, Proc. Amer. Math. Soc. 125, No 11 (1997), 3169-3176.
%F a(4*n-3) = A271231(4*n-3), a(4*n-2) = 0, a(4*n-1) = -A271231(4*n-1), a(4*n) = 0.
%F G.f.: x * Product_{k>0} (1 - x^(2*k)) * (1 - x^(4*k)) * (1 - x^(6*k)) * (1 - x^(12*k)).
%F a(2*n+1) = A030188(n). - _Michel Marcus_, Sep 25 2016
%F Euler transform of period 12 sequence [0, -1, 0, -2, 0, -2, 0, -2, 0, -1, 0, -4, ...]. - _Georg Fischer_, Nov 17 2022
%t CoefficientList[Series[QPochhammer[x^2] QPochhammer[x^4] QPochhammer[x^6] QPochhammer[x^12], {x, 0, 100}], x] (* _Jan Mangaldan_, Jan 04 2017 *)
%Y Cf. A030188, A271231, A276807, A276649.
%K sign,mult
%O 1,5
%A _Seiichi Manyama_, Sep 22 2016