A290271 Expansion of j(q) * q * Product_{n>=1} (1+q^n)^24 where j(q) is the elliptic modular invariant (A000521).

1, 768, 215040, 26444800, 1441185792, 47967398400, 1138440560640, 21001337579520, 317833282191360, 4093417325768448, 46062726364262400, 461921554374159360, 4191623003406663680, 34838889359457538560, 267847934788735057920

Offset

0,2

Links

Seiichi Manyama, Table of n, a(n) for n = 0..1000

Steven R. Finch, Modular forms on SL_2(Z), December 28, 2005. [Cached copy, with permission of the author]

Formula

Let b(q) = q * Product_{n>=1} (1+q^n)^24.

G.f.: j(q) * b(q) = (1 + 256*b(q))^3.

a(n) ~ 3^(1/4) * exp(2*Pi*sqrt(6*n)) / (4096 * 2^(3/4) * n^(3/4)). - Vaclav Kotesovec, Jul 26 2017

Mathematica

nmax = 20; CoefficientList[Series[(1 + 256*x*Product[(1 + x^k)^24, {k, 1, nmax}])^3, {x, 0, nmax}], x] (* Vaclav Kotesovec, Jul 26 2017 *)

Crossrefs

Cf. A000521, A014103 (b(q)).

Sequence in context: A268970 A339763 A204625 * A206711 A308789 A046505

Adjacent sequences: A290268 A290269 A290270 * A290272 A290273 A290274

Keyword

nonn

Author

Seiichi Manyama, Jul 25 2017

Status

approved