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 A370712 a(n) = 3^n * [x^n] Product_{k>=1} (1 + 3*x^k)^(1/3). 4
 1, 3, 0, 99, -270, 2430, -10287, 105462, -750141, 5702481, -42623901, 347424633, -2779077762, 22353287634, -181730796723, 1493711042589, -12321529794261, 102125312638713, -850797139405887, 7120067746384863, -59800770201017934, 503922807927384129, -4259721779079782751 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 LINKS Table of n, a(n) for n=0..22. FORMULA G.f.: Product_{k>=1} (1 + 3*(3*x)^k)^(1/3). a(n) ~ (-1)^(n+1) * c * 9^n / n^(4/3), where c = QPochhammer(-1/3)^(1/3) / (3*Gamma(2/3)) = 0.26286302373105271371291957730496322329245126572... MATHEMATICA nmax = 30; CoefficientList[Series[Product[(1 + 3*x^k), {k, 1, nmax}]^(1/3), {x, 0, nmax}], x] * 3^Range[0, nmax] nmax = 30; CoefficientList[Series[Product[(1 + 3*(3*x)^k), {k, 1, nmax}]^(1/3), {x, 0, nmax}], x] nmax = 30; CoefficientList[Series[(QPochhammer[-3, x]/4)^(1/3), {x, 0, nmax}], x] * 3^Range[0, nmax] CROSSREFS Cf. A032308, A370710. Cf. A300579, A344062. Sequence in context: A013243 A013244 A322458 * A372314 A266380 A076951 Adjacent sequences: A370709 A370710 A370711 * A370713 A370714 A370715 KEYWORD sign AUTHOR Vaclav Kotesovec, Feb 27 2024 STATUS approved

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Last modified August 8 17:42 EDT 2024. Contains 375023 sequences. (Running on oeis4.)