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%I #12 Jun 11 2017 04:37:44
%S 1,-2,0,0,8,-12,0,0,39,-56,0,0,152,-208,0,0,513,-684,0,0,1560,-2032,0,
%T 0,4382,-5616,0,0,11552,-14592,0,0,28899,-36088,0,0,69168,-85500,0,0,
%U 159372,-195312,0,0,355224,-431984,0,0,768885,-928720,0,0,1621296,-1946352,0,0,3339201
%N Expansion of eta(q)^2 / (eta(q^2) * eta(q^4)^6) in powers of q.
%H Seiichi Manyama, <a href="/A134414/b134414.txt">Table of n, a(n) for n = -1..1000</a>
%H K. Bringmann and K. Ono, <a href="http://dx.doi.org/10.1090/S0002-9939-07-08883-1">An arithmetic formula for the partition function</a>, Proc Am. Math. Soc. 135 (2007), 3507-3514. see p. 3507 Equ. (1.2).
%F Euler transform of period 4 sequence [ -2, -1, -2, 5, ...].
%F a(4*n+1) = a(4*n+2) = 0.
%F G.f.: x^(-1) * Product_{k>0} (1 - x^k) / ((1 + x^k) * (1 - x^(4*k))^6).
%e 1/q - 2 + 8*q^3 - 12*q^4 + 39*q^7 - 56*q^8 + 152*q^11 - 208*q^12 + ...
%t QP = QPochhammer; s = QP[q]^2/(QP[q^2]*QP[q^4]^6) + O[q]^60; CoefficientList[s, q] (* _Jean-François Alcover_, Nov 27 2015 *)
%o (PARI) {a(n) = local(A); if( n<-1, 0, n++; A = x * O(x^n); polcoeff( eta(x + A)^2 / (eta(x^2 + A) * eta(x^4 + A)^6), n))}
%Y A134415(n) = a(4*n-1). -2 * A134416(n) = a(4*n).
%K sign
%O -1,2
%A _Michael Somos_, Oct 26 2007