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Expansion of Product_{k>=1} (1 - 2*x^k)/(1 + 2*x^k).
2

%I #13 Apr 25 2018 03:00:21

%S 1,-4,4,-4,20,-36,52,-116,244,-500,964,-1876,3876,-7780,15332,-30628,

%T 61684,-123460,246036,-491988,985492,-1971284,3939556,-7878068,

%U 15762692,-31527428,63041220,-126078916,252185044,-504375460,1008698036,-2017385268,4034873268

%N Expansion of Product_{k>=1} (1 - 2*x^k)/(1 + 2*x^k).

%F a(n) ~ c * (-2)^n, where c = QPochhammer[-1, -1/2]/QPochhammer[-1/2] = 0.93943604828296530723602398257349307281... - _Vaclav Kotesovec_, Apr 25 2018

%t nmax = 40; CoefficientList[Series[Product[(1 - 2*x^k)/(1 + 2*x^k), {k, 1, nmax}], {x, 0, nmax}], x] (* _Vaclav Kotesovec_, Apr 25 2018 *)

%o (PARI) N=66; x='x+O('x^N); Vec(prod(k=1, N, (1-2*x^k)/(1+2*x^k)))

%Y Expansion of Product_{k>=1} (1 - b*x^k)/(1 + b*x^k): A002448 (b=1), this sequence (b=2), A303398 (b=3).

%Y Cf. A261584, A303345.

%K sign

%O 0,2

%A _Seiichi Manyama_, Apr 23 2018