A299862 Coefficients in expansion of (E_6^2/E_4^3)^(1/32).

1, -54, -5022, -3259116, -1012953978, -479848911192, -201506019745716, -93655132040105136, -43096009052844972522, -20449878102745826555178, -9772372681245342509703768, -4732826670479844302345499132, -2309711500786845517082643561660

Offset

0,2

Links

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

Formula

G.f.: (1 - 1728/j)^(1/32), where j is the j-function.

a(n) ~ c * exp(2*Pi*n) / n^(17/16), where c = -3^(1/32) * Gamma(1/4)^(1/4) / (2^(17/4) * Pi^(3/16) * Gamma(15/16)) = -0.0582176906417343821471376177620947... - Vaclav Kotesovec, Mar 04 2018

a(n) * A299949(n) ~ -sin(Pi/16) * exp(4*Pi*n) / (16*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)^(1/32) + 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), this sequence (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: A368366 A291071 A254620 * A342893 A007761 A178633

Adjacent sequences: A299859 A299860 A299861 * A299863 A299864 A299865

Keyword

sign

Author

Seiichi Manyama, Feb 21 2018

Status

approved