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%I #9 Dec 10 2017 05:03:54
%S 1,-3,2,-4,14,-11,6,-20,21,-14,10,-16,38,-20,14,-40,43,-42,16,-28,62,
%T -43,22,-40,74,-42,26,-40,64,-68,28,-80,98,-63,34,-52,110,-62,32,-100,
%U 133,-70,42,-56,108,-80,46,-120,112,-114,50,-72,158,-84,54,-140,183
%N Expansion of q^(-1/3) * eta(q)^3 * eta(q^3)^3 / eta(q^2)^2 in powers of q.
%H G. C. Greubel, <a href="/A279261/b279261.txt">Table of n, a(n) for n = 0..1000</a>
%F Euler transform of period 6 sequence [ -3, -1, -6, -1, -3, -4, ...].
%F 3 * a(n) = A260301(3*n + 1).
%e G.f. = 1 - 3*x + 2*x^2 - 4*x^3 + 14*x^4 - 11*x^5 + 6*x^6 - 20*x^7 + ...
%e G.f. = q - 3*q^4 + 2*q^7 - 4*q^10 + 14*q^13 - 11*q^16 + 6*q^19 + ...
%t a[ n_] := SeriesCoefficient[ QPochhammer[ x]^3 QPochhammer[ x^3]^3 / 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)^3 / eta(x^2 + A)^2, n))};
%Y Cf. A260301.
%K sign
%O 0,2
%A _Michael Somos_, Dec 08 2016
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