A284286 - OEIS

%I #83 Feb 21 2021 03:59:56

%S 1,8,40,160,552,1712,4896,13120,33320,80872,188784,425952,932640,

%T 1988080,4137024,8422848,16810536,32943760,63482760,120440608,

%U 225217904,415498496,756920160,1362645440,2425895712,4273590392,7454092720,12879684160,22056267840

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

%H Seiichi Manyama, <a href="/A284286/b284286.txt">Table of n, a(n) for n = 0..10000</a>

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

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

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

%t eta = QPochhammer;

%t CoefficientList[eta[q^2]^4/eta[q]^8 + O[q]^30, q] (* _Jean-François Alcover_, Feb 21 2021 *)

%o (Julia) # JacobiTheta4 is defined in A002448.

%o A284286List(len) = JacobiTheta4(len, -4)

%o A284286List(29) |> println # _Peter Luschny_, Mar 12 2018

%Y Column k=4 of A288515.

%Y Cf. A002131, A004405, A096727.

%K nonn

%O 0,2

%A _Seiichi Manyama_, May 02 2017