cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A024299 a(n) = (2*n)! [x^(2*n)] log(1 + tanh(x)^2)/2.

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%I A024299 #31 Jul 12 2022 17:24:06
%S A024299 0,1,-14,496,-34544,4055296,-724212224,183218384896,-62380415842304,
%T A024299 27507260369207296,-15250924309151350784,10384039093607251050496,
%U A024299 -8517991922318587187953664,8285309769460200661892202496,-9429010285390912531529354706944
%N A024299 a(n) = (2*n)! [x^(2*n)] log(1 + tanh(x)^2)/2.
%H A024299 G. C. Greubel, <a href="/A024299/b024299.txt">Table of n, a(n) for n = 0..215</a>
%F A024299 a(n) = A009403(n)/2.
%F A024299 a(n) = -2^(2*n-1)*(4^n - 2)*(4^n - 1)*zeta(1-2*n) for n >= 1. - _Peter Luschny_, Oct 29 2020
%p A024299 a := n -> `if`(n=0, 0, -2^(2*n-1)*(4^n-2)*(4^n-1)*Zeta(1-2*n)):
%p A024299 seq(a(n), n=0..14); # _Peter Luschny_, Oct 29 2020
%t A024299 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 *)
%o A024299 (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
%o A024299 (Magma)
%o A024299 L:=RiemannZeta();
%o A024299 [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
%o A024299 (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
%Y A024299 Cf. A009403.
%Y A024299 Cf. A003707, A101921.
%K A024299 sign
%O A024299 0,3
%A A024299 _R. H. Hardin_
%E A024299 Extended with signs, Mar 1997
%E A024299 Previous Mathematica program replaced by _Harvey P. Dale_, Dec 12 2021