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%I #8 Feb 08 2018 13:50:43
%S 1,0,-1,-1,-3,1,1,3,2,-2,5,-1,1,-2,-4,-2,-3,2,-7,-2,4,7,0,-1,-1,0,4,
%T 10,5,-7,7,-3,-6,-3,0,-1,-5,-6,3,-7,1,5,-5,1,-4,1,-9,7,2,16,2,-2,8,2,
%U 5,2,5,-11,-4,-1,1,1,-2,2,6,-12,7,-9,-9,1,-15,-2,1,-4
%N Expansion of q^(-13/24) * eta(q^2) * eta(q^3) * eta(q^4)^2 in powers of q.
%F Euler transform of period 12 sequence [0, -1, -1, -3, 0, -2, 0, -3, -1, -1, 0, -4, ...].
%F G.f.: Product_{k>0} (1 - x^(2*k)) * (1 - x^(3*k)) * (1 - x^(4*k))^2.
%e G.f. = 1 - x^2 - x^3 - 3*x^4 + x^5 + x^6 + 3*x^7 + 2*x^8 - 2*x^9 + ...
%e G.f. = q^13 - q^61 - q^85 - 3*q^109 + q^133 + q^157 + 3*q^181 + 2*q^205 + ...
%t a[ n_] := SeriesCoefficient[ QPochhammer[ x^2] QPochhammer[ x^3] QPochhammer[ x^4]^2, {x, 0, n}]; (* _Michael Somos_, Sep 07 2015 *)
%o (PARI) {a(n) = my(A); if( n<0, 0, A = x * O(x^n); polcoeff( eta(x^2 + A) * eta(x^3 + A) * eta(x^4 + A)^2, n))};
%K sign
%O 0,5
%A _Michael Somos_, Jul 27 2008
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