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A298411
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Coefficients of q^(-1/24)*eta(4q)^(1/2).
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6
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1, -2, -10, -20, -90, 132, -836, 6040, 2310, 60180, 180308, 1662568, -2995620, 24401320, 44072120, -102437328, 19390406, 2649221300, -10584460060, 14475802440, -228570333836, -815899620616, 2088529753800, -5590702681520, -100828534100580, -172013432412024
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OFFSET
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0,2
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COMMENTS
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The q^(kn) term of any single factor of the product (1-(4q)^k)^(1/2) is (-2)*A000108(n-1). Hence these numbers are related to the Catalan numbers A000108 by a partition-based convolution.
Sequence appears to be positive and negative roughly half the time.
This sequence is obtained from the generalized Euler transform in A266964 by taking f(n) = -1/2, g(n) = 4^n. - Seiichi Manyama, Apr 20 2018
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LINKS
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FORMULA
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G.f.: Product_{k>=1} (1 - (4x)^k)^(1/2).
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MATHEMATICA
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Series[Product[(1 - (4 q)^k)^(1/2), {k, 1, 100}], {q, 0, 100}]
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PROG
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(PARI) q='q+O('q^99); Vec(eta(4*q)^(1/2)) \\ Altug Alkan, Apr 20 2018
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CROSSREFS
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KEYWORD
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sign,easy
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AUTHOR
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STATUS
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approved
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