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 A298411 Coefficients of q^(-1/24)*eta(4q)^(1/2). 6
 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS 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 LINKS Seiichi Manyama, Table of n, a(n) for n = 0..1000 FORMULA G.f.: Product_{k>=1} (1 - (4x)^k)^(1/2). MATHEMATICA Series[Product[(1 - (4 q)^k)^(1/2), {k, 1, 100}], {q, 0, 100}] PROG (PARI) q='q+O('q^99); Vec(eta(4*q)^(1/2)) \\ Altug Alkan, Apr 20 2018 CROSSREFS Cf. A000108, A271235, A298994. Expansion of Product_{n>=1} (1 - ((b^2)*x)^n)^(1/b): A010815 (b=1), this sequence (b=2), A303152 (b=3), A303153 (b=4), A303154 (b=5). Sequence in context: A090220 A164882 A029994 * A324474 A294493 A261660 Adjacent sequences:  A298408 A298409 A298410 * A298412 A298413 A298414 KEYWORD sign,easy AUTHOR William J. Keith, Jan 18 2018 STATUS approved

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Last modified September 21 20:10 EDT 2021. Contains 347598 sequences. (Running on oeis4.)