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%I #9 Dec 17 2017 22:05:50
%S 0,1,1,0,-5,-15,46,735,2185,-33390,-453479,-364155,57806200,681966285,
%T -3289884779,-197798065920,-1815938249585,33917006295885,
%U 1155429901407646,5691720408045315,-408736165211351795,-10271257189100959590,23948813753053818421,6626731340918542069425,124356774945741129842320
%N Expansion of e.g.f. arcsinh(exp(x)-1).
%H Robert Israel, <a href="/A296545/b296545.txt">Table of n, a(n) for n = 0..440</a>
%F E.g.f.: -log(1 - exp(x) + sqrt(1 + (1 - exp(x))^2)).
%e arcsinh(exp(x)-1) = x/1! + x^2/2! - 5*x^4/4! - 15*x^5/5! + 46*x^6/6! + 735*x^7/7! + ...
%p S:= series(arcsinh(exp(x)-1),x,41):
%p seq(coeff(S,x,j)*j!,j=0..40); # _Robert Israel_, Dec 17 2017
%t nmax = 24; CoefficientList[Series[ArcSinh[Exp[x] - 1], {x, 0, nmax}], x] Range[0, nmax]!
%t nmax = 24; CoefficientList[Series[-Log[1 - Exp[x] + Sqrt[1 + (1 - Exp[x])^2]], {x, 0, nmax}], x] Range[0, nmax]!
%Y Cf. A014307, A024429, A121868.
%K sign
%O 0,5
%A _Ilya Gutkovskiy_, Dec 15 2017
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