A293378 Expansion of (eta(q^6)/(eta(q)*eta(q^2)*eta(q^3)))^2 in powers of q.

1, 2, 7, 16, 39, 80, 171, 328, 638, 1168, 2133, 3744, 6540, 11092, 18687, 30816, 50421, 81136, 129582, 204160, 319340, 493952, 758781, 1154624, 1745748, 2617958, 3902614, 5776144, 8501784, 12434320, 18092565, 26175784, 37689734, 53989056, 76993497, 109284736

Offset

0,2

Links

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

Formula

G.f.: Product_{k>0} ((1 - x^(6*k))/((1 - x^k)*(1 - x^(2*k))*(1 - x^(3*k))))^2.

a(n) ~ 5^(5/4) * exp(2*Pi*sqrt(5*n)/3) / (72 * sqrt(3) * n^(7/4)). - Vaclav Kotesovec, Oct 11 2017

Mathematica

nmax = 50; CoefficientList[Series[Product[((1 + x^(3*k))/((1 - x^k)*(1 - x^(2*k))))^2, {k, 1, nmax}], {x, 0, nmax}], x] (* Vaclav Kotesovec, Oct 11 2017 *)

Crossrefs

Cf. A077285, A293377.

Sequence in context: A224227 A260505 A042243 * A377728 A041887 A129441

Adjacent sequences: A293375 A293376 A293377 * A293379 A293380 A293381

Keyword

nonn

Author

Seiichi Manyama, Oct 07 2017

Status

approved