%I #15 Oct 15 2016 03:22:57
%S 1,-2,-5,10,13,-22,-30,40,60,-78,-101,132,170,-210,-273,342,409,-514,
%T -625,748,917,-1102,-1300,1570,1863,-2186,-2589,3034,3540,-4148,-4838,
%U 5584,6489,-7500,-8621,9958,11417,-13046,-14960,17066,19417,-22122,-25119,28450,32253,-36478
%N Expansion of q^(-3/4) * eta(q)^2 * eta(q^2)^4 * eta(q^8)^4 / eta(q^4)^6 in powers of q.
%H G. C. Greubel, <a href="/A135467/b135467.txt">Table of n, a(n) for n = 0..1000</a>
%H T. Ishikawa, <a href="http://projecteuclid.org/euclid.hmj/1206128505">Congruences between binomial coefficients binom(2f,f) and Fourier coefficients of certain eta-products</a>, Hiroshima Math. J. 22 (1992), no. 3, 583-590.
%F Euler transform of period 8 sequence [ -2, -6, -2, 0, -2, -6, -2, -4, ...]. - _Michael Somos_, Mar 01 2008
%e q^3 - 2*q^7 - 5*q^11 + 10*q^15 + 13*q^19 - 22*q^23 - 30*q^27 + ...
%t QP = QPochhammer; s = QP[q]^2*QP[q^2]^4*(QP[q^8]^4/QP[q^4]^6) + O[q]^50; CoefficientList[s, q] (* _Jean-François Alcover_, Nov 27 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^2 + A)^2 / eta(x^4 + A)^3 * eta(x^8 + A)^2)^2, n))} /* _Michael Somos_, Mar 01 2008 */
%K sign
%O 0,2
%A _N. J. A. Sloane_, Feb 07 2008