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 A370716 a(n) = 3^(2*n) * [x^n] Product_{k>=1} (1 + 2*x^k)^(1/3). 6
 1, 6, 18, 1170, -1890, 133326, 101250, 20498994, -164656314, 3778220862, -28085954094, 771567716970, -10691904063114, 183594050113518, -2711145260068326, 49416883617381354, -789899109743435994, 13176840267952166070, -216403389726994588086, 3681309971143060236810 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 LINKS Table of n, a(n) for n=0..19. FORMULA G.f.: Product_{k>=1} (1 + 2*(9*x)^k)^(1/3). a(n) ~ (-1)^(n+1) * c * 18^n / n^(4/3), where c = QPochhammer(-1/2)^(1/3) / (3*Gamma(2/3)) = 0.2623638446186535909018671540030519... MATHEMATICA nmax = 20; CoefficientList[Series[Product[(1 + 2*x^k), {k, 1, nmax}]^(1/3), {x, 0, nmax}], x] * 3^(2*Range[0, nmax]) nmax = 20; CoefficientList[Series[Product[(1 + 2*(9*x)^k), {k, 1, nmax}]^(1/3), {x, 0, nmax}], x] nmax = 20; CoefficientList[Series[(QPochhammer[-2, x]/3)^(1/3), {x, 0, nmax}], x] * 3^(2*Range[0, nmax]) CROSSREFS Cf. A032302, A370715. Cf. A075900, A300581, A304961, A327550. Sequence in context: A372522 A130437 A119813 * A119986 A245869 A370155 Adjacent sequences: A370713 A370714 A370715 * A370717 A370718 A370719 KEYWORD sign AUTHOR Vaclav Kotesovec, Feb 27 2024 STATUS approved

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Last modified August 14 15:00 EDT 2024. Contains 375165 sequences. (Running on oeis4.)