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%I #3 Nov 29 2019 13:21:25
%S 1,-3,2,-2,8,-7,2,-4,7,-10,2,-2,16,-10,6,-4,7,-16,4,-6,16,-15,6,-4,12,
%T -10,6,-6,24,-20,4,-4,12,-21,6,-6,24,-26,4,-8,13,-10,10,-8,32,-10,6,
%U -12,12,-32,6,-4,32,-26,10,-4,13,-30,10,-10,24,-20,8,-8,24
%N Expansion of q^(-1/3) * eta(q)^3 * eta(q^3) * eta(q^6) / eta(q^2)^2 in powers of q.
%F Euler transform of period 6 sequence [-3, -1, -4, -1, -3, -3, ...].
%F G.f.: Product_{k>=1} (1 - x^(2*k)) * (1 - x^(3*k)) * (1 - x^(6*k)) / (1 - x^k)^3.
%F A329955(3*n + 1) = -a(n).
%e G.f. = 1 - 3*x + 2*x^2 - 2*x^3 + 8*x^4 - 7*x^5 + 2*x^6 - 4*x^7 + ...
%e G.f. = q - 3*q^4 + 2*q^7 - 2*q^10 + 8*q^13 - 7*q^16 + 2*q^19 - 4*q^22 + ...
%t a[ n_] := SeriesCoefficient[ QPochhammer[ x]^3 QPochhammer[ x^3] QPochhammer[ x^6] / QPochhammer[ x^2]^2, {x, 0, n}];
%o (PARI) {a(n) = my(A); if( n<0, 0, A = x * O(x^n); polcoeff( eta(x + A)^3 * eta(x^3 + A) * eta(x^6 + A) / eta(x^2 + A)^2, n))};
%Y Cf. A329955.
%K sign
%O 0,2
%A _Michael Somos_, Nov 29 2019
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