login
A284286
Expansion of eta(q^2)^4 / eta(q)^8 in powers of q.
6
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
0,2
LINKS
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 *)
PROG
(Julia) # JacobiTheta4 is defined in A002448.
A284286List(len) = JacobiTheta4(len, -4)
A284286List(29) |> println # Peter Luschny, Mar 12 2018
CROSSREFS
Column k=4 of A288515.
Sequence in context: A128639 A341365 A004405 * A001789 A074412 A364619
KEYWORD
nonn
AUTHOR
Seiichi Manyama, May 02 2017
STATUS
approved