A290403 - OEIS

A290403

Expansion of 256/(lambda(z)*(1 - lambda(z)))^2 in powers of nome q = exp(Pi*i*z) where lambda(z) is the elliptic modular function (A115977).

1, 48, 1128, 17344, 196884, 1766496, 13105152, 83077248, 461646786, 2295171024, 10380853248, 43297436352, 168383270616, 616088091552, 2136382808064, 7063702309504, 22381414626687, 68246605486224, 200988391505920, 573443411403648, 1589242581740388

(list; graph; refs; listen; history; text; internal format)

OFFSET

-2,2

LINKS

Table of n, a(n) for n=-2..18.

Eric Weisstein's World of Mathematics, Elliptic Lambda Function

FORMULA

Expansion of (eta(q^2)^2 / (eta(q) * eta(q^4)))^48 in powers of q.

a(n) ~ exp(2*Pi*sqrt(2*n)) / (2^(3/4)*n^(3/4)). - Vaclav Kotesovec, Jul 30 2017

MATHEMATICA

nmax = 20; CoefficientList[Series[Product[(1 + x^(2*k-1))^48, {k, 1, nmax}], {x, 0, nmax}], x] (* Vaclav Kotesovec, Jul 30 2017 *)

CROSSREFS

Cf. A014972 (1/(1 - lambda)), A029845 (16/lambda), A097340 (16/(lambda*(1 - lambda))).

Cf. A000521, A000700, A115977, A290404.

Sequence in context: A022077 A010964 A287991 * A035719 A035797 A213442

Adjacent sequences: A290400 A290401 A290402 * A290404 A290405 A290406

KEYWORD

nonn

AUTHOR

Seiichi Manyama, Jul 30 2017

STATUS

approved