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 A370711 a(n) = 4^n * [x^n] Product_{k>=1} (1 + 3*x^k)^(1/2). 4
 1, 6, 6, 348, -570, 12084, -31332, 780792, -6111930, 65506884, -599418444, 6707736456, -69508986852, 738378468744, -7878832564872, 85524000547056, -929068361832378, 10158667075255524, -111690827626777788, 1234592278534799592, -13700571880245603276, 152613494540593338264 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 LINKS Table of n, a(n) for n=0..21. FORMULA G.f.: Product_{k>=1} (1 + 3*(4*x)^k)^(1/2). a(n) ~ (-1)^(n+1) * c * 12^n / n^(3/2), where c = QPochhammer(-1/3)^(1/2) / (2*sqrt(Pi)) = 0.311283382185276347775502154581850436407169685238... MATHEMATICA nmax = 30; CoefficientList[Series[Product[(1 + 3*x^k), {k, 1, nmax}]^(1/2), {x, 0, nmax}], x] * 4^Range[0, nmax] nmax = 30; CoefficientList[Series[Product[(1 + 3*(4*x)^k), {k, 1, nmax}]^(1/2), {x, 0, nmax}], x] nmax = 30; CoefficientList[Series[Sqrt[QPochhammer[-3, x]/4], {x, 0, nmax}], x] * 4^Range[0, nmax] CROSSREFS Cf. A032308, A370714. Cf. A300579, A344062. Sequence in context: A244956 A239532 A351793 * A165641 A213149 A267727 Adjacent sequences: A370708 A370709 A370710 * A370712 A370713 A370714 KEYWORD sign AUTHOR Vaclav Kotesovec, Feb 27 2024 STATUS approved

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Last modified August 3 11:52 EDT 2024. Contains 374888 sequences. (Running on oeis4.)