A296614 Coefficients in expansion of (E_6^2/E_4^3)^(1/96).

1, -18, -1998, -1156356, -382624794, -177898412808, -76229340502932, -35444571049682064, -16446161396159063082, -7832755937588033655054, -3761678744155185551186328, -1828621496185972561746774324, -895757692814150533920101726460

Offset

0,2

Links

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

Formula

G.f.: (1 - 1728/j)^(1/96).

a(n) ~ -Gamma(1/4)^(1/12) * exp(2*Pi*n) / (16 * 2^(1/12) * 3^(95/96) * Pi^(1/16) * Gamma(47/48) * n^(49/48)). - Vaclav Kotesovec, Mar 04 2018

a(n) * A299696(n) ~ -sin(Pi/48) * exp(4*Pi*n) / (48*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)^(1/96) + O[x]^terms // CoefficientList[#, x]& (* Jean-François Alcover, Feb 26 2018 *)

Crossrefs

(E_6^2/E_4^3)^(k/288): A289366 (k=1), A296609 (k=2), this sequence (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), A299414 (k=96), A299413 (k=144), A289210 (k=288).

Cf. A000521 (j), A299696.

Sequence in context: A249332 A019522 A068181 * A341842 A230818 A276017

Adjacent sequences: A296611 A296612 A296613 * A296615 A296616 A296617

Keyword

sign

Author

Seiichi Manyama, Feb 15 2018

Status

approved