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A030220 Expansion of (eta(q^3)*eta(q^5))^3 in powers of q.

%I A030220 #18 Jun 03 2016 11:06:19
%S A030220 1,0,0,-3,0,-3,0,0,9,5,0,0,0,0,-15,5,0,0,-22,0,0,0,0,21,25,0,0,0,0,0,
%T A030220 2,0,0,-14,0,-27,0,0,0,-35,0,0,0,0,0,34,0,0,49,0,42,0,0,-27,0,0,0,0,0,
%U A030220 45,-118,0,0,13,0,0,0,0,-102,0,0,0,0,0,0,66,0,0,98,0,81,0,0,0,-70,0,0,0,0,45,0,0,0,-14
%N A030220 Expansion of (eta(q^3)*eta(q^5))^3 in powers of q.
%H A030220 Seiichi Manyama, <a href="/A030220/b030220.txt">Table of n, a(n) for n = 1..10000</a>
%H A030220 M. Koike, <a href="http://projecteuclid.org/euclid.nmj/1118787564">On McKay's conjecture</a>, Nagoya Math. J., 95 (1984), 85-89.
%F A030220 Euler transform of period 15 sequence [ 0, 0, -3, 0, -3, -3, 0, 0, -3, -3, 0, -3, 0, 0, -6, ...]. - _Michael Somos_, Jun 14 2007
%F A030220 G.f.: (1/2)* Sum_{u,v} (u*u -4*v*v)* x^(u*u +u*v +4*v*v). - _Michael Somos_, Jun 14 2007
%F A030220 G.f.: x*(Product_{k>0} (1-x^(3*k))(1-x^(5*k)))^3. - _Michael Somos_, Jun 14 2007
%e A030220 q - 3*q^4 - 3*q^6 + 9*q^9 + 5*q^10 - 15*q^15 + 5*q^16 - 22*q^19 + 21*q^24 + ...
%t A030220 QP = QPochhammer; s = (QP[q^3]*QP[q^5])^3 + O[q]^100; CoefficientList[s, q] (* _Jean-François Alcover_, Nov 25 2015 *)
%K A030220 sign
%O A030220 1,4
%A A030220 _N. J. A. Sloane_, Dec 11 1999