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 A370715 a(n) = 3^(2*n) * [x^n] Product_{k>=1} 1/(1 - 2*x^k)^(1/3). 5
 1, 6, 126, 1818, 32130, 452142, 8006526, 117619290, 1999520154, 31550881374, 527781570174, 8556328428786, 145177242834330, 2404855490356782, 40907085509085750, 691705559193384114, 11840743106503713594, 202344257179543757526, 3487245860820904368822, 60077736592697832105330 (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/(1 - 2*(9*x)^k)^(1/3). a(n) ~ c * 18^n / n^(2/3), where c = 1 / (Gamma(1/3) * QPochhammer(1/2)^(1/3)) = 0.564734286036917647642848904946237... MATHEMATICA nmax = 25; CoefficientList[Series[Product[1/(1-2*x^k), {k, 1, nmax}]^(1/3), {x, 0, nmax}], x] * 9^Range[0, nmax] nmax = 25; CoefficientList[Series[Product[1/(1-2*(9*x)^k), {k, 1, nmax}]^(1/3), {x, 0, nmax}], x] nmax = 25; CoefficientList[Series[(-1/QPochhammer[2, x])^(1/3), {x, 0, nmax}], x] * 9^Range[0, nmax] CROSSREFS Cf. A070933, A370716. Sequence in context: A268685 A109820 A228290 * A004993 A237428 A255900 Adjacent sequences: A370712 A370713 A370714 * A370716 A370717 A370718 KEYWORD nonn AUTHOR Vaclav Kotesovec, Feb 27 2024 STATUS approved

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Last modified August 9 05:47 EDT 2024. Contains 375027 sequences. (Running on oeis4.)