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

0,4

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

Formula

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

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 *)

Crossrefs

Cf. A013973 (E_6), A045828.

Sequence in context: A375002 A053348 A019256 * A014969 A139820 A241204

Adjacent sequences: A286396 A286397 A286398 * A286400 A286401 A286402

Keyword

nonn

Author

Seiichi Manyama, May 08 2017

Status

approved