A303491 Expansion of Product_{k>=1} ((1 - 8^k*x^k)/(1 + 8^k*x^k))^(1/8^k).
1, -2, 0, -42, 86, -1638, 1428, -71286, 218592, -3941590, 5374096, -187901262, 661408902, -10769651242, 18007942140, -597519823962, 2262843922694, -34034727280806, 65527429637360, -1858398841872062, 7543997928104274, -118580678725935186
Offset: 0
Keywords
Links
- Seiichi Manyama, Table of n, a(n) for n = 0..1000
Programs
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Mathematica
nmax = 30; CoefficientList[Series[Exp[Sum[(1 - (-1)^j) / (j*(1 - 1/(8^(j-1)*x^j))), {j, 1, nmax}]], {x, 0, nmax}], x] (* Vaclav Kotesovec, Apr 25 2018 *) -
PARI
N=66; x='x+O('x^N); Vec(prod(k=1, N, ((1-8^k*x^k)/(1+8^k*x^k))^(1/8^k)))
Formula
G.f.: exp(Sum_{j>=1} ((1 - (-1)^j) / (j*(1 - 1/(8^(j-1)*x^j))) )). - Vaclav Kotesovec, Apr 25 2018