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%I #23 Sep 08 2022 08:45:00
%S 1,-1,-1,2,-2,-2,6,-3,-5,12,-8,-9,24,-14,-18,42,-26,-31,76,-45,-54,
%T 126,-76,-88,210,-121,-144,332,-196,-225,526,-302,-351,804,-464,-531,
%U 1224,-698,-800,1818,-1040,-1179,2688,-1519,-1728,3902,-2212,-2491,5632,-3167,-3571,8016,-4508
%N Expansion of g.f. Product_{n>=1} (1-x^n)*(1-x^(5*n))/(1-x^(3*n))^2.
%H G. C. Greubel, <a href="/A054274/b054274.txt">Table of n, a(n) for n = 0..1000</a>
%H A. J. Guttmann, <a href="https://doi.org/10.1016/S0012-365X(99)00262-9">Indicators of solvability for lattice models</a>, Discrete Math., 217 (2000), 167-189.
%F Euler transform of period 15 sequence [ -1, -1, 1, -1, -2, 1, -1, -1, 1, -2, -1, 1, -1, -1, 0, ...]. - _Michael Somos_, Sep 21 2005
%F Expansion of eta(q)*eta(q^5)/eta(q^3)^2 in powers of q. - _Michael Somos_, Sep 21 2005
%e G.f. = 1 - q - q^2 + 2*q^3 - 2*q^4 - 2*q^5 + 6*q^6 - 3*q^7 - 5*q^8 + 12*q^9 + ...
%t QP = QPochhammer; s = QP[q]*(QP[q^5]/QP[q^3]^2) + O[q]^60; CoefficientList[ s, q] (* _Jean-François Alcover_, Nov 30 2015, adapted from PARI *)
%o (PARI) {a(n)=local(A); if(n<0, 0, A=x*O(x^n); polcoeff( eta(x+A)* eta(x^5+A)/eta(x^3+A)^2, n))} /* _Michael Somos_, Sep 21 2005 */
%o (Magma) m:=60; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!( (&*[(1-x^j)*(1-x^(5*j))/(1-x^(3*j))^2: j in [1..m+2]]) )); // _G. C. Greubel_, Jul 31 2019
%K sign
%O 0,4
%A _N. J. A. Sloane_, May 08 2000
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