A299422 Coefficients in expansion of (E_6^2/E_4^3)^(1/36).

1, -48, -4608, -2926656, -919916544, -434180785824, -182989456349184, -85043754451706496, -39190139442556010496, -18607302407649844554480, -8899353903793993480829952, -4312672556860403013966227136, -2105991149652021429396842987520

Offset

0,2

Links

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

Formula

G.f.: (1 - 1728/j)^(1/36), where j is the j-function.

a(n) ~ c * exp(2*Pi*n) / n^(19/18), where c = -Gamma(1/4)^(2/9) / (2^(11/9) * 3^(71/36) * Pi^(1/6) * Gamma(17/18)) = -0.0521763497905021090549912315961203... - Vaclav Kotesovec, Mar 04 2018

a(n) * A299943(n) ~ -sin(Pi/18) * exp(4*Pi*n) / (18*Pi*n^2). - Vaclav Kotesovec, Mar 04 2018

Mathematica

terms = 13;
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)^(1/36) + O[x]^terms // CoefficientList[#, x]& (* Jean-François 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), this sequence (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), A299414 (k=96), A299413 (k=144), A289210 (k=288).

Cf. A000521 (j).

Sequence in context: A208793 A174755 A269419 * A321940 A364174 A222846

Adjacent sequences: A299419 A299420 A299421 * A299423 A299424 A299425

Keyword

sign

Author

Seiichi Manyama, Feb 21 2018

Status

approved