A286399 Expansion of eta(q^2)^12 * eta(q^4)^8 / eta(q)^8 in powers of q.

0, 0, 1, 8, 32, 96, 244, 528, 1024, 1856, 3126, 5016, 7808, 11616, 16808, 23856, 32768, 44352, 59293, 77352, 100032, 128128, 161052, 201264, 249856, 305280, 371294, 450128, 537856, 640992, 762744, 894528, 1048576, 1228224, 1419858, 1642080, 1897376, 2167008

Offset: 0

Author

Seiichi Manyama, May 08 2017

Keywords

• nonn

Comments

The average order of a(n) is n^5 * Pi^6 / 30720. - Vaclav Kotesovec, Feb 09 2023

Links

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

Crossrefs

Cf. A013973 (E_6), A045828.

Programs

Mathematica

CoefficientList[x^2 * Series[QPochhammer[x^2]^12 * QPochhammer[x^4]^8 / QPochhammer[x]^8, {x, 0, 40}], x] (* Vaclav Kotesovec, Feb 08 2023 *)

Formula

G.f.: x^2 * Product_{k>0} (1 - x^(2 * k))^12 * (1 - x^(4 * k))^8 / (1 - x^k)^8.