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 A327682 Expansion of Product_{k>0} (-1+sqrt(1+4*x^k))/(2*x^k). 3
 1, -1, 1, -5, 14, -40, 122, -404, 1362, -4608, 15881, -55709, 197402, -705114, 2539282, -9210196, 33605471, -123262137, 454268676, -1681305246, 6246544735, -23288217459, 87096982499, -326680267261, 1228547420236, -4631474743422, 17499462106763, -66257720483935, 251356773101419 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,4 LINKS Seiichi Manyama, Table of n, a(n) for n = 0..1000 FORMULA a(n) ~ (-1)^n * c * 4^n / n^(3/2), where c = 1/(2*sqrt(Pi)) * Product_{k>=1} (-1 + sqrt(1 + 4*(-1/4)^k)) / (2*(-1/4)^k) = 0.5396673413761086071059510679780476790558662471136055... - Vaclav Kotesovec, May 06 2021 MATHEMATICA m = 28; CoefficientList[Series[Product[(-1 + Sqrt[1 + 4*x^k])/(2*x^k), {k, 1, m}], {x, 0, m}], x] (* Amiram Eldar, May 06 2021 *) PROG (PARI) N=66; x='x+O('x^N); Vec(prod(k=1, N, (-1+sqrt(1+4*x^k))/(2*x^k))) (PARI) N=66; x='x+O('x^N); Vec(prod(i=1, N, sum(j=0, N\i, (-1)^j*binomial(2*j, j)*x^(i*j)/(j+1)))) CROSSREFS Cf. A000108, A081362, A168491, A309867, A322204, A327683. Sequence in context: A184437 A023871 A274598 * A171185 A122485 A198086 Adjacent sequences: A327679 A327680 A327681 * A327683 A327684 A327685 KEYWORD sign AUTHOR Seiichi Manyama, Sep 22 2019 STATUS approved

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Last modified December 4 07:54 EST 2023. Contains 367557 sequences. (Running on oeis4.)