A288844 Coefficients of the modular function j_3 = j^3 - 2232*j^2 + 1069956*j - 36866976.

1, 0, 0, 0, 2592899910, 12756069900288, 9529320689550144, 2622941159057326080, 378428749397345529225, 34379738365334381035520, 2195434131954412557737088, 105922359559684281299632128, 4060690624555940636889532470

Offset

-3,5

Links

Seiichi Manyama, Table of n, a(n) for n = -3..1000

K. Ono, A mock theta function for the Delta-function, Proceedings of the 2007 Integers Conference, Carrollton, Georgia, October 24—27, 2007.

Formula

a(n) ~ 3^(1/4) * exp(4*Pi*sqrt(3*n)) / (sqrt(2)*n^(3/4)). - Vaclav Kotesovec, Jun 29 2017

Example

G.f.: 1/q^3 + 2592899910*q + 12756069900288*q^2 + 9529320689550144*q^3 + 2622941159057326080*q^4 + ...

Mathematica

a[ n_] := With[{j = 1728 KleinInvariantJ[ Log[q]/(2 Pi I)]}, SeriesCoefficient[ Series[ j^3 - 2232 j^2 + 1069956 j - 36866976, {q, 0, n + 2}], {q, 0, n}]]; (* Michael Somos, Aug 15 2018 *)

Crossrefs

Cf. A014708 (j_1), A288843 (j_2), this sequence (j_3).

Cf. A000521 (j), A028515 ((q*j)^2), A288846 ((q*j)^3).

Sequence in context: A308377 A271105 A134439 * A028521 A064163 A022230

Adjacent sequences: A288841 A288842 A288843 * A288845 A288846 A288847

Keyword

nonn

Author

Seiichi Manyama, Jun 18 2017

Status

approved