A296545 - OEIS

%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