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A299414 Coefficients in expansion of (E_6^2/E_4^3)^(1/3). 19
1, -576, 96768, -30253824, 4526272512, -1917275819904, 105679295281152, -161582272076127744, -20815321809392861184, -20529723592970845750080, -6560883968194298456036352, -3617226648349298247150473472 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

Seiichi Manyama, Table of n, a(n) for n = 0..367

FORMULA

G.f.: (1 - 1728/j)^(1/3), where j is the j-function.

a(n) ~ -Gamma(1/4)^(8/3) * exp(2*Pi*n) / (2^(5/3) * 3^(2/3) * Pi^2 * Gamma(1/3) * n^(5/3)). - Vaclav Kotesovec, Mar 04 2018

a(n) * A300054(n) ~ -exp(4*Pi*n) / (sqrt(3)*Pi*n^2). - Vaclav Kotesovec, Mar 04 2018

MATHEMATICA

terms = 12;

E4[x_] = 1 + 240*Sum[k^3*x^k/(1 - x^k), {k, 1, terms}] + O[x]^terms;

E6[x_] = 1 - 504*Sum[k^5*x^k/(1 - x^k), {k, 1, terms}] + O[x]^terms; (E6[x]^2/E4[x]^3)^(1/3) + O[x]^terms // CoefficientList[#, x]& (* Jean-François Alcover, Feb 22 2018 *)

CROSSREFS

(E_6^2/E_4^3)^(k/288): A289366 (k=1), A296609 (k=2), A296614 (k=3), A296652 (k=4), A297021 (k=6), A299422 (k=8), A299862 (k=9), A289368 (k=12), A299856 (k=16), A299857 (k=18), A299858 (k=24), A299863 (k=32), A299859 (k=36), A299860 (k=48), A299861 (k=72), this sequence (k=96), A299413 (k=144), A289210 (k=288).

Cf. A000521 (j), A289340, A299831.

Sequence in context: A268903 A249688 A079396 * A300054 A013775 A068277

Adjacent sequences: A299411 A299412 A299413 * A299415 A299416 A299417

KEYWORD

sign

AUTHOR

Seiichi Manyama, Feb 21 2018

STATUS

approved

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Last modified November 29 18:13 EST 2022. Contains 358431 sequences. (Running on oeis4.)