A284286 - OEIS

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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

(list; graph; refs; listen; history; text; internal format)

OFFSET

0,2

LINKS

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

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.

MATHEMATICA

eta = QPochhammer;

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