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 A319672 a(n) = [x^n] Product_{k>=2} ((1 + x^k)/(1 - x^k))^n. 1
 1, 0, 4, 6, 40, 110, 520, 1778, 7568, 28320, 116224, 453046, 1837600, 7306234, 29565848, 118786526, 481192480, 1945153838, 7895908852, 32046260282, 130370798320, 530650047710, 2163191769336, 8824509524082, 36037768384832, 147277910160160, 602398740105712, 2465582764631334 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 LINKS Vaclav Kotesovec, Table of n, a(n) for n = 0..1000 FORMULA a(n) = [x^n] ((1 - x)/((1 + x)*theta_4(x)))^n, where theta_4() is the Jacobi theta function. a(n) = [x^n] exp(n*Sum_{k>=1} (sigma(2*k) - sigma(k) + (-1)^k - 1)*x^k/k). a(n) ~ c * d^n / sqrt(n), where d = 4.16958962845360844086951404338054148667024... and c = 0.23380422010834870751549442953816486722... - Vaclav Kotesovec, Oct 06 2018 MATHEMATICA Table[SeriesCoefficient[Product[((1 + x^k)/(1 - x^k))^n , {k, 2, n}], {x, 0, n}], {n, 0, 27}] Table[SeriesCoefficient[((1 - x)/((1 + x) EllipticTheta[4, 0, x]))^n, {x, 0, n}], {n, 0, 27}] 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}] CROSSREFS Cf. A000203, A270919, A300415, A319670, A319671. Sequence in context: A175349 A281223 A023644 * A355233 A145387 A034923 Adjacent sequences: A319669 A319670 A319671 * A319673 A319674 A319675 KEYWORD nonn AUTHOR Ilya Gutkovskiy, Sep 25 2018 STATUS approved

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Last modified June 5 19:06 EDT 2023. Contains 363138 sequences. (Running on oeis4.)