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%I #7 Mar 27 2019 03:50:25
%S 0,1,-1,4,-18,118,-930,8888,-98504,1248784,-17790480,281590032,
%T -4901447232,93064850448,-1914144990576,42396742460928,
%U -1006101059149440,25466710774651776,-684902462140798848,19503187752732408576,-586221766070655432960
%N Expansion of e.g.f. arctanh(log(1 + x)).
%e arctanh(log(1 + x)) = x^1/1! - x^2/2! + 4*x^3/3! - 18*x^4/4! + 118*x^5/5! - 930*x^6/6! + ...
%p a:=series(arctanh(log(1+x)),x=0,21): seq(n!*coeff(a,x,n),n=0..20); # _Paolo P. Lava_, Mar 26 2019
%t nmax = 20; CoefficientList[Series[ArcTanh[Log[1 + x]], {x, 0, nmax}], x] Range[0, nmax]!
%t nmax = 20; CoefficientList[Series[Log[1 + Log[1 + x]]/2 - Log[1 - Log[1 + x]]/2, {x, 0, nmax}], x] Range[0, nmax]!
%Y Cf. A001710, A003703, A003708, A009024, A009454, A009775, A010050, A104150, A202139, A296979, A296980, A296981.
%K sign
%O 0,4
%A _Ilya Gutkovskiy_, Dec 22 2017
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