A299859 Coefficients in expansion of (E_6^2/E_4^3)^(1/8).

1, -216, -2592, -10412064, -1955812608, -1193816824272, -424976182312320, -205525905843878208, -89308328381644142592, -42098146869799454214456, -19580168925118916335723968, -9345687920591466548039096160

Offset

0,2

Links

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

Formula

G.f.: (1 - 1728/j)^(1/8), where j is the j-function.

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

a(n) * A299994(n) ~ -exp(4*Pi*n) / (4*sqrt(2)*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)^(1/8) + 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), this sequence (k=36), A299860 (k=48), A299861 (k=72), A299414 (k=96), A299413 (k=144), A289210 (k=288).

Cf. A000521 (j).

Sequence in context: A243862 A223559 A017055 * A017139 A249005 A249470

Adjacent sequences: A299856 A299857 A299858 * A299860 A299861 A299862

Keyword

sign

Author

Seiichi Manyama, Feb 21 2018

Status

approved