A319553 - OEIS

%I #18 Sep 24 2018 09:50:27

%S 1,16,144,960,5264,25056,106944,418176,1520784,5201232,16871648,

%T 52252992,155341248,445226848,1234726272,3323392128,8704504976,

%U 22234655520,55498917840,135595345600,324759439584,763505859072,1764050361152,4009763323008,8975341703616,19800832628336

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

%H Seiichi Manyama, <a href="/A319553/b319553.txt">Table of n, a(n) for n = 0..10000</a>

%F Convolution inverse of A035016.

%F a(n) = (-1)^n * A004409(n).

%F a(0) = 1, a(n) = (16/n)*Sum_{k=1..n} A002131(k)*a(n-k) for n > 0.

%F G.f.: Product_{k>=1} ((1 - x^(2k))/(1 - x^k)^2)^8.

%o (PARI) N=99; x='x+O('x^N); Vec(prod(k=1, N, ((1-x^(2*k))/(1-x^k)^2)^8))

%Y 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 Cf. A002131, A002448 (theta_4(q)), A004409, A035016.

%K nonn

%O 0,2

%A _Seiichi Manyama_, Sep 22 2018