A284286 Expansion of eta(q^2)^4 / eta(q)^8 in powers of q.

1, 8, 40, 160, 552, 1712, 4896, 13120, 33320, 80872, 188784, 425952, 932640, 1988080, 4137024, 8422848, 16810536, 32943760, 63482760, 120440608, 225217904, 415498496, 756920160, 1362645440, 2425895712, 4273590392, 7454092720, 12879684160, 22056267840

Offset: 0

Author

Seiichi Manyama, May 02 2017

Keywords

• nonn

Links

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

Crossrefs

Column k=4 of A288515.

Cf. A002131, A004405, A096727.

Programs

Julia

# JacobiTheta4 is defined in A002448.
A284286List(len) = JacobiTheta4(len, -4)
A284286List(29) |> println # Peter Luschny, Mar 12 2018

Mathematica

eta = QPochhammer;
CoefficientList[eta[q^2]^4/eta[q]^8 + O[q]^30, q] (* Jean-François Alcover, Feb 21 2021 *)

Formula

a(n) = (-1)^n * A004405(n).

a(0) = 1, a(n) = (8/n)*Sum_{k=1..n} A002131(k)*a(n-k) for n > 0.

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