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A290271 Expansion of j(q) * q * Product_{n>=1} (1+q^n)^24 where j(q) is the elliptic modular invariant (A000521). 1
1, 768, 215040, 26444800, 1441185792, 47967398400, 1138440560640, 21001337579520, 317833282191360, 4093417325768448, 46062726364262400, 461921554374159360, 4191623003406663680, 34838889359457538560, 267847934788735057920 (list; graph; refs; listen; history; text; internal format)
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

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Last modified October 21 19:16 EDT 2021. Contains 348155 sequences. (Running on oeis4.)