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A319553 Expansion of 1/theta_4(q)^8 in powers of q = exp(Pi i t).

%I A319553 #18 Sep 24 2018 09:50:27
%S A319553 1,16,144,960,5264,25056,106944,418176,1520784,5201232,16871648,
%T A319553 52252992,155341248,445226848,1234726272,3323392128,8704504976,
%U A319553 22234655520,55498917840,135595345600,324759439584,763505859072,1764050361152,4009763323008,8975341703616,19800832628336
%N A319553 Expansion of 1/theta_4(q)^8 in powers of q = exp(Pi i t).
%H A319553 Seiichi Manyama, <a href="/A319553/b319553.txt">Table of n, a(n) for n = 0..10000</a>
%F A319553 Convolution inverse of A035016.
%F A319553 a(n) = (-1)^n * A004409(n).
%F A319553 a(0) = 1, a(n) = (16/n)*Sum_{k=1..n} A002131(k)*a(n-k) for n > 0.
%F A319553 G.f.: Product_{k>=1} ((1 - x^(2k))/(1 - x^k)^2)^8.
%o A319553 (PARI) N=99; x='x+O('x^N); Vec(prod(k=1, N, ((1-x^(2*k))/(1-x^k)^2)^8))
%Y A319553 1/theta_4(q)^b: A015128 (b=1), A001934 (b=2), A319552 (b=3), A284286 (b=4), this sequence (b=8), A319554 (b=12).
%Y A319553 Cf. A002131, A002448 (theta_4(q)), A004409, A035016.
%K A319553 nonn
%O A319553 0,2
%A A319553 _Seiichi Manyama_, Sep 22 2018