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%I #9 Oct 06 2018 08:04:45
%S 1,0,4,6,40,110,520,1778,7568,28320,116224,453046,1837600,7306234,
%T 29565848,118786526,481192480,1945153838,7895908852,32046260282,
%U 130370798320,530650047710,2163191769336,8824509524082,36037768384832,147277910160160,602398740105712,2465582764631334
%N a(n) = [x^n] Product_{k>=2} ((1 + x^k)/(1 - x^k))^n.
%H Vaclav Kotesovec, <a href="/A319672/b319672.txt">Table of n, a(n) for n = 0..1000</a>
%F a(n) = [x^n] ((1 - x)/((1 + x)*theta_4(x)))^n, where theta_4() is the Jacobi theta function.
%F a(n) = [x^n] exp(n*Sum_{k>=1} (sigma(2*k) - sigma(k) + (-1)^k - 1)*x^k/k).
%F a(n) ~ c * d^n / sqrt(n), where d = 4.16958962845360844086951404338054148667024... and c = 0.23380422010834870751549442953816486722... - _Vaclav Kotesovec_, Oct 06 2018
%t Table[SeriesCoefficient[Product[((1 + x^k)/(1 - x^k))^n , {k, 2, n}], {x, 0, n}], {n, 0, 27}]
%t Table[SeriesCoefficient[((1 - x)/((1 + x) EllipticTheta[4, 0, x]))^n, {x, 0, n}], {n, 0, 27}]
%t Table[SeriesCoefficient[Exp[n Sum[(DivisorSigma[1, 2 k] - DivisorSigma[1, k] + (-1)^k - 1) x^k/k, {k, 1, n}]], {x, 0, n}], {n, 0, 27}]
%Y Cf. A000203, A270919, A300415, A319670, A319671.
%K nonn
%O 0,3
%A _Ilya Gutkovskiy_, Sep 25 2018
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