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A181977
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Expansion of b(q) * c(q^3)^2 / 9 in powers of q where b(), c() are cubic AGM theta functions.
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1
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1, -3, 0, 8, -9, 0, 17, -27, 0, 40, -39, 0, 50, -72, 0, 96, -81, 0, 104, -150, 0, 176, -153, 0, 170, -243, 0, 280, -216, 0, 273, -360, 0, 400, -351, 0, 362, -510, 0, 560, -450, 0, 520, -648, 0, 736, -615, 0, 601, -864, 0, 936, -729, 0, 850, -1086, 0, 1160
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OFFSET
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2,2
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COMMENTS
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LINKS
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FORMULA
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Expansion of (eta(q) * eta(q^9)^2 / eta(q^3))^3 in powers of q.
Euler transform of period 9 sequence [-3, -3, 0, -3, -3, 0, -3, -3, -6, ...].
a(3*n + 1) = 0. a(3*n) = -3 * A106402(n).
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EXAMPLE
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G.f. = q^2 - 3*q^3 + 8*q^5 - 9*q^6 + 17*q^8 - 27*q^9 + 40*q^11 - 39*q^12 + ...
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MATHEMATICA
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eta[q_]:= q^(1/24)*QPochhammer[q]; CoefficientList[Series[(eta[q]* eta[q^9]^2/eta[q^3])^3, {q, 0, 50}], q] (* G. C. Greubel, Aug 11 2018 *)
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PROG
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(PARI) {a(n) = my(A); if( n<2, 0, n = n-2; A = x * O(x^n); polcoeff( (eta(x + A) * eta(x^9 + A)^2 / eta(x^3 + A))^3, n))};
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CROSSREFS
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KEYWORD
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sign
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AUTHOR
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STATUS
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approved
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