A299413 Coefficients in expansion of (E_6^2/E_4^3)^(1/2).

1, -864, 269568, -75240576, 19930724352, -5124295980864, 1292387210099712, -321604751662509312, 79241739168490536960, -19376923061550541800672, 4709786462808256974509568, -1139188440993923671697455488

Offset

0,2

Links

Seiichi Manyama, Table of n, a(n) for n = 0..422

Formula

G.f.: (1 - 1728/j)^(1/2), where j is the j-function.

a(n) ~ (-1)^n * c * exp(Pi*sqrt(3)*n) * sqrt(n), where c = 32*sqrt(2) * Pi^(11/2) / Gamma(1/3)^9. - Vaclav Kotesovec, Mar 04 2018

Mathematica

terms = 12;
E4[x_] = 1 + 240*Sum[k^3*x^k/(1 - x^k), {k, 1, terms}] + O[x]^terms;
E6[x_] = 1 - 504*Sum[k^5*x^k/(1 - x^k), {k, 1, terms}] + O[x]^terms; (E6[x]^2/E4[x]^3)^(1/2) + O[x]^terms // CoefficientList[#, x]& (* Jean-François Alcover, Feb 22 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), A299860 (k=48), A299861 (k=72), A299414 (k=96), this sequence (k=144), A289210 (k=288).

Cf. A000521 (j), A007242, A299832.

Sequence in context: A300034 A064321 A210408 * A300055 A082243 A308131

Adjacent sequences: A299410 A299411 A299412 * A299414 A299415 A299416

Keyword

sign

Author

Seiichi Manyama, Feb 21 2018

Status

approved