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A319552 Expansion of 1/theta_4(q)^3 in powers of q = exp(Pi i t).

%I A319552 #24 Sep 24 2018 09:40:07
%S A319552 1,6,24,80,234,624,1552,3648,8184,17654,36816,74544,147056,283440,
%T A319552 535008,990912,1803882,3232224,5707624,9943536,17106960,29088352,
%U A319552 48922320,81438528,134261584,219336630,355242288,570675904,909674688,1439394192,2261635168,3529838208
%N A319552 Expansion of 1/theta_4(q)^3 in powers of q = exp(Pi i t).
%H A319552 Seiichi Manyama, <a href="/A319552/b319552.txt">Table of n, a(n) for n = 0..10000</a>
%F A319552 Convolution inverse of A213384.
%F A319552 a(n) = (-1)^n * A004404(n).
%F A319552 a(0) = 1, a(n) = (6/n)*Sum_{k=1..n} A002131(k)*a(n-k) for n > 0.
%F A319552 G.f.: Product_{k>=1} ((1 - x^(2k))/(1 - x^k)^2)^3.
%o A319552 (PARI) N=99; x='x+O('x^N); Vec(prod(k=1, N, ((1-x^(2*k))/(1-x^k)^2)^3))
%Y A319552 1/theta_4(q)^b: A015128 (b=1), A001934 (b=2), this sequence (b=3), A284286 (b=4), A319553 (b=8), A319554 (b=12).
%Y A319552 Cf. A002131, A002448 (theta_4(q)), A004404, A213384.
%K A319552 nonn
%O A319552 0,2
%A A319552 _Seiichi Manyama_, Sep 22 2018