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Expansion of Product_{k>=1} ((1 + (4^k*x)^k)/(1 - (4^k*x)^k))^(1/4^k).
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%I #10 Apr 25 2018 05:55:22

%S 1,2,34,8268,33571414,2199090644476,2305847408435939284,

%T 38685630839429196310146392,10384593794440986129804618334166246,

%U 44601490417830435032541177335778584157585132,3064991081820980697863893053179715579559319341564967996,3369993333399959956498356892070248429341537193850764394491913892776

%N Expansion of Product_{k>=1} ((1 + (4^k*x)^k)/(1 - (4^k*x)^k))^(1/4^k).

%H Seiichi Manyama, <a href="/A303444/b303444.txt">Table of n, a(n) for n = 0..41</a>

%F a(n) ~ 2^(2*n^2 - 2*n + 1). - _Vaclav Kotesovec_, Apr 25 2018

%o (PARI) N=20; x='x+O('x^N); Vec(prod(k=1, N, ((1+(4^k*x)^k)/(1-(4^k*x)^k))^(1/4^k)))

%Y Cf. A303440, A303445.

%K nonn

%O 0,2

%A _Seiichi Manyama_, Apr 24 2018