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%I #22 Jul 12 2022 17:24:32
%S 0,2,-28,992,-69088,8110592,-1448424448,366436769792,-124760831684608,
%T 55014520738414592,-30501848618302701568,20768078187214502100992,
%U -17035983844637174375907328,16570619538920401323784404992
%N Expansion of e.g.f. log(1 + tanh(x)^2), even powers only.
%H Vincenzo Librandi, <a href="/A009403/b009403.txt">Table of n, a(n) for n = 0..100</a>
%F a(n) ~ (-1)^(n+1) * 2^(4*n) * (2*n)! / (n * Pi^(2*n)). - _Vaclav Kotesovec_, Apr 20 2014
%F From _G. C. Greubel_, Jul 12 2022: (Start)
%F a(n) = 2*A024299(n).
%F a(n) = -4^n * (4^n - 2)*(4^n - 1)*Zeta(1-2*n), with a(0) = 0. (End)
%t With[{nn=30},Take[CoefficientList[Series[Log[1+Tanh[x]^2],{x,0,nn}],x] Range[0,nn]!,{1,-1,2}]] (* _Harvey P. Dale_, Aug 27 2013 *)
%o (Magma)
%o L:=RiemannZeta();
%o [0] cat [-Round(4^n*(4^n-2)*(4^n-1)*Evaluate(L, 1-2*n)): n in [1..20]]; // _G. C. Greubel_, Jul 12 2022
%o (SageMath) [0]+[-4^n*(4^n-2)*(4^n-1)*zeta(1-2*n) for n in (1..20)] # _G. C. Greubel_, Jul 12 2022
%Y Cf. A024299.
%K sign
%O 0,2
%A _R. H. Hardin_
%E Extended with signs by _Olivier Gérard_, Mar 15 1997
%E Previous Mathematica program replaced by _Harvey P. Dale_, Aug 27 2013
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