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 A289340 Coefficients of (q*(j(q)-1728))^(1/3) where j(q) is the elliptic modular invariant. 2
 1, -328, -41956, -8596032, -2597408634, -916285828640, -352170121921992, -143129703441671168, -60517599938503137519, -26355020095077489965264, -11743692598044815023990588, -5329748160859504303225598464 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS In general, the expansion of (q*(j(q)-1728))^m, where j(q) is the elliptic modular invariant (A000521), and m <> 0, is asymptotic to exp(4*Pi*sqrt(m*n)) * m^(1/4) / (sqrt(2) * n^(3/4)) if 2*m is the positive integer, else is asymptotic to 2^(2*m) * 3^(4*m) * Pi^(2*m) * exp(2*Pi*(n-m)) / (Gamma(-2*m) * Gamma(3/4)^(8*m) * n^(2*m + 1)). - Vaclav Kotesovec, Mar 07 2018 LINKS FORMULA G.f.: Product_{k>=1} (1-q^k)^(A289061(k)/3). a(n) ~ c * exp(2*Pi*n) / n^(5/3), where c = -2^(2/3) * 3^(5/6) * exp(-2*Pi/3) * Gamma(2/3) / (Pi^(1/3) * Gamma(3/4)^(8/3)) = -0.262554753987597280323546158564... - Vaclav Kotesovec, Mar 07 2018 MATHEMATICA CoefficientList[Series[((256/QPochhammer[-1, x]^8 + x*QPochhammer[-1, x]^16/256)^3 - 1728*x)^(1/3), {x, 0, 20}], x] (* Vaclav Kotesovec, Mar 07 2018 *) CROSSREFS (q*(j(q)-1728))^(k/24): A106203 (k=1), A289330 (k=2), A289331 (k=3), A289332 (k=4), A289333 (k=5), A289334 (k=6), A289339 (k=7), this sequence (k=8), A007242 (k=12), A289063 (k=24). Cf. A289061. Sequence in context: A138078 A232140 A231130 * A252004 A278352 A246858 Adjacent sequences:  A289337 A289338 A289339 * A289341 A289342 A289343 KEYWORD sign AUTHOR Seiichi Manyama, Jul 02 2017 STATUS approved

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Last modified June 23 08:25 EDT 2021. Contains 345395 sequences. (Running on oeis4.)