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%I #9 Mar 27 2019 03:50:19
%S 0,1,-1,0,6,-22,-30,952,-5656,-9952,508320,-3874992,-20690208,
%T 833780400,-7697940432,-52230156288,2467649024640,-24686997151104,
%U -329724479772288,14493628861307136,-159114034671287040,-2682505451050592256,126421889770129637376
%N Expansion of e.g.f. arctan(log(1 + x)).
%F a(n) ~ (-1)^(n+1) * (n-1)! * sin(n*(Pi-1)/2) / (2 - 2*cos(1))^(n/2). - _Vaclav Kotesovec_, Mar 26 2019
%e arctan(log(1 + x)) = x^1/1! - x^2/2! + 6*x^4/4! - 22*x^5/5! - 30*x^6/6! + ...
%p a:=series(arctan(log(1+x)),x=0,23): seq(n!*coeff(a,x,n),n=0..22); # _Paolo P. Lava_, Mar 26 2019
%t nmax = 22; CoefficientList[Series[ArcTan[Log[1 + x]], {x, 0, nmax}], x] Range[0, nmax]!
%t nmax = 22; CoefficientList[Series[(I/2) Log[1 - I Log[1 + x]] - (I/2) Log[1 + I Log[1 + x]], {x, 0, nmax}], x] Range[0, nmax]!
%Y Cf. A001710, A003703, A003708, A009024, A009454, A009775, A010050, A104150, A110708, A296979, A296980, A296982.
%K sign
%O 0,5
%A _Ilya Gutkovskiy_, Dec 22 2017
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