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Expansion of Product_{k>=1} (1 - 4*x^k)/(1 + 4*x^k).
2

%I #11 Apr 25 2018 02:56:41

%S 1,-8,24,-72,344,-1416,5400,-21576,87000,-348296,1390872,-5560776,

%T 22253784,-89025672,356055960,-1424186568,5696931032,-22787865096,

%U 91150729368,-364602357960,1458412314456,-5833651510536,23334594559128,-93338369011272,373353522099288

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

%F a(n) ~ c * (-4)^n, where c = QPochhammer[-1, -1/4]/QPochhammer[-1/4] = 1.3264181585010678966173808329272239860188791629... - _Vaclav Kotesovec_, Apr 25 2018

%t nmax = 30; CoefficientList[Series[Product[(1 - 4*x^k)/(1 + 4*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, (1-4*x^k)/(1+4*x^k)))

%Y Expansion of Product_{k>=1} (1 - b*x^k)/(1 + b*x^k): A002448 (b=1), A303397 (b=2), A303398 (b=3), this sequence (b=4).

%Y Cf. A303387, A303391.

%K sign

%O 0,2

%A _Seiichi Manyama_, Apr 23 2018