A293389 Expansion of ((eta(q)eta(q^3))/eta(q^2)^2)^2 in powers of q.

1, -2, 3, -8, 15, -24, 39, -64, 102, -152, 225, -336, 492, -700, 987, -1392, 1941, -2664, 3630, -4936, 6660, -8896, 11817, -15648, 20604, -26942, 35070, -45512, 58800, -75576, 96777, -123568, 157206, -199200, 251613, -316992, 398148, -498460, 622356, -775216

Offset

0,2

Links

Seiichi Manyama, Table of n, a(n) for n = 0..10000

Formula

G.f.: Product_{k>0} (((1 - x^k)*(1 - x^(3*k)))/(1 - x^(2*k))^2)^2.

a(n) ~ (-1)^n * exp(2*Pi*sqrt(2*n)/3) / (2^(3/4) * 3^(3/2) * n^(3/4)). - Vaclav Kotesovec, Oct 08 2017

Mathematica

nmax = 100; CoefficientList[Series[Product[(1 - x^(3*k))^2 / ((1 + x^k)^4 * (1 - x^k)^2), {k, 1, nmax}], {x, 0, nmax}], x] (* Vaclav Kotesovec, Oct 08 2017 *)

Crossrefs

Main diagonal of A293388.

Cf. A293306, A293387.

Sequence in context: A365413 A174019 A356371 * A128035 A003473 A095373

Adjacent sequences: A293386 A293387 A293388 * A293390 A293391 A293392

Keyword

sign

Author

Seiichi Manyama, Oct 08 2017

Status

approved