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A299856 Coefficients in expansion of (E_6^2/E_4^3)^(1/18). 19
1, -96, -6912, -5410944, -1537640448, -753077521728, -307254291047424, -143134552425743616, -65142005576276164608, -30798673631132393592288, -14628259811568672073824768, -7054762801208507859522653568 (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)^(1/18), where j is the j-function.

a(n) ~ c * exp(2*Pi*n) / n^(10/9), where c = -Gamma(1/4)^(4/9) / (2^(4/9) * 3^(35/18) * Pi^(1/3) * Gamma(8/9)) = -0.0974650059642735838539936939997471425... - Vaclav Kotesovec, Mar 04 2018

a(n) * A299950(n) ~ -sin(Pi/9) * exp(4*Pi*n) / (9*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}];

E6[x_] = 1 - 504*Sum[k^5*x^k/(1 - x^k), {k, 1, terms}];

(E6[x]^2/E4[x]^3)^(1/18) + O[x]^terms // CoefficientList[#, x]& (* Jean-Fran├žois Alcover, Feb 28 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), this sequence (k=16), A299857 (k=18), A299858 (k=24), A299863 (k=32), A299859 (k=36), A299860 (k=48), A299861 (k=72), A299414 (k=96), A299413 (k=144), A289210 (k=288).

Cf. A000521 (j).

Sequence in context: A229585 A093296 A093248 * A270603 A000545 A189909

Adjacent sequences:  A299853 A299854 A299855 * A299857 A299858 A299859

KEYWORD

sign

AUTHOR

Seiichi Manyama, Feb 21 2018

STATUS

approved

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Last modified November 28 12:36 EST 2021. Contains 349403 sequences. (Running on oeis4.)