A299860 Coefficients in expansion of (E_6^2/E_4^3)^(1/6).

1, -288, 6912, -13136256, -1543993344, -1312510191552, -400771816381440, -207423640540991232, -85808962187667652608, -40835278880374417949088, -18652791316021929491056128, -8871850083830324974981015680

Offset

0,2

Links

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

Formula

G.f.: (1 - 1728/j)^(1/6), where j is the j-function.

a(n) ~ -Gamma(1/4)^(4/3) * exp(2*Pi*n) / (2^(4/3) * 3^(5/6) * Pi * Gamma(2/3) * n^(4/3)). - Vaclav Kotesovec, Mar 04 2018

a(n) * A300052(n) ~ -exp(4*Pi*n) / (2*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}];
E6[x_] = 1 - 504*Sum[k^5*x^k/(1 - x^k), {k, 1, terms}];
(E6[x]^2/E4[x]^3)^(1/6) + 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), A299422 (k=8), A299862 (k=9), A289368 (k=12), A299856 (k=16), A299857 (k=18), A299858 (k=24), A299863 (k=32), A299859 (k=36), this sequence (k=48), A299861 (k=72), A299414 (k=96), A299413 (k=144), A289210 (k=288).

Cf. A000521 (j).

Sequence in context: A232340 A290028 A330817 * A264204 A202165 A264001

Adjacent sequences: A299857 A299858 A299859 * A299861 A299862 A299863

Keyword

sign

Author

Seiichi Manyama, Feb 21 2018

Status

approved