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%I #12 Nov 25 2015 12:18:36
%S 1,-8,20,0,-70,64,56,0,-133,-96,148,0,670,-512,-968,0,1077,1680,-2064,
%T 0,-2098,768,4400,0,-1766,-8128,7044,0,744,4096,-4760,0,-9780,16344,
%U -6652,0,7894,-13440,-10320,0,41923,-8736,-16780,0,-5892,-6144,14560,0,-27886,-11056,55940
%N Expansion of q^(-3) * (eta(q) * eta(q^8))^8 in powers of q.
%H Alois P. Heinz, <a href="/A034433/b034433.txt">Table of n, a(n) for n = 0..1000</a>
%F Euler transform of period 8 sequence [ -8, -8, -8, -8, -8, -8, -8, -16, ...]. - _Michael Somos_, Nov 11 2007
%F a(4*n+3) = 0.
%e q^3 - 8*q^4 + 20*q^5 - 70*q^7 + 64*q^8 + 56*q^9 - 133*q^11 - 96*q^12 + ...
%t QP = QPochhammer; s = (QP[q]*QP[q^8])^8 + O[q]^60; CoefficientList[s, q] (* _Jean-François Alcover_, Nov 25 2015 *)
%o (PARI) {a(n) = local(A); if( n<0, 0, A = x * O(x^n); polcoeff( ( eta(x + A) * eta(x^8 + A) )^8, n))} /* _Michael Somos_, Nov 11 2007 */
%Y -8 * A002288(n) = a(4*n-3).
%K sign
%O 0,2
%A _N. J. A. Sloane_
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