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A276847
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Expansion of eta(q^2) * eta(q^4) * eta(q^6) * eta(q^12) in powers of q.
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1
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1, 0, -1, 0, -2, 0, 0, 0, 1, 0, 4, 0, -2, 0, 2, 0, 2, 0, -4, 0, 0, 0, -8, 0, -1, 0, -1, 0, 6, 0, 8, 0, -4, 0, 0, 0, 6, 0, 2, 0, -6, 0, 4, 0, -2, 0, 0, 0, -7, 0, -2, 0, -2, 0, -8, 0, 4, 0, 4, 0, -2, 0, 0, 0, 4, 0, -4, 0, 8, 0, 8, 0, 10, 0, 1, 0, 0, 0, -8, 0, 1, 0
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OFFSET
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1,5
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COMMENTS
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The bisection of this sequence containing all nonzero terms is A030188.
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LINKS
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FORMULA
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a(4*n-3) = A271231(4*n-3), a(4*n-2) = 0, a(4*n-1) = -A271231(4*n-1), a(4*n) = 0.
G.f.: x * Product_{k>0} (1 - x^(2*k)) * (1 - x^(4*k)) * (1 - x^(6*k)) * (1 - x^(12*k)).
Euler transform of period 12 sequence [0, -1, 0, -2, 0, -2, 0, -2, 0, -1, 0, -4, ...]. - Georg Fischer, Nov 17 2022
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MATHEMATICA
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CoefficientList[Series[QPochhammer[x^2] QPochhammer[x^4] QPochhammer[x^6] QPochhammer[x^12], {x, 0, 100}], x] (* Jan Mangaldan, Jan 04 2017 *)
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CROSSREFS
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KEYWORD
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sign,mult
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AUTHOR
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STATUS
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approved
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