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A024299
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a(n) = (2*n)! [x^(2*n)] log(1 + tanh(x)^2)/2.
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4
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0, 1, -14, 496, -34544, 4055296, -724212224, 183218384896, -62380415842304, 27507260369207296, -15250924309151350784, 10384039093607251050496, -8517991922318587187953664, 8285309769460200661892202496, -9429010285390912531529354706944
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OFFSET
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0,3
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LINKS
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FORMULA
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a(n) = -2^(2*n-1)*(4^n - 2)*(4^n - 1)*zeta(1-2*n) for n >= 1. - Peter Luschny, Oct 29 2020
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MAPLE
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a := n -> `if`(n=0, 0, -2^(2*n-1)*(4^n-2)*(4^n-1)*Zeta(1-2*n)):
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MATHEMATICA
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With[{nn=30}, Take[CoefficientList[Series[Log[1+Tanh[x]^2]/2, {x, 0, nn}], x] Range[0, nn]!, {1, -1, 2}]] (* Harvey P. Dale, Dec 12 2021 *)
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PROG
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(PARI) my(x='x+O('x^30), v = concat([0, 0], Vec(serlaplace (log(1+tanh(x)^2)/2)))); vector(#v\2, k, v[2*k-1]) \\ Michel Marcus, Oct 29 2020
(Magma)
L:=RiemannZeta();
[0] cat [-Round(2^(2*n-1)*(4^n-2)*(4^n-1)*Evaluate(L, 1-2*n)): n in [1..15]]; // G. C. Greubel, Jul 12 2022
(SageMath) [0]+[-2^(2*n-1)*(4^n-2)*(4^n-1)*zeta(1-2*n) for n in (1..15)] # G. C. Greubel, Jul 12 2022
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CROSSREFS
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KEYWORD
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sign
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AUTHOR
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EXTENSIONS
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Extended with signs, Mar 1997
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STATUS
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approved
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