%I #13 Mar 27 2019 10:04:55
%S 0,1,2,5,20,109,654,4353,34824,324441,3244410,34795485,417545820,
%T 5536151685,77506123590,1144330385625,18309286170000,315366695240625,
%U 5676600514331250,106667957800963125,2133359156019262500,45229212438054868125,995042673637207098750,22696937952367956440625
%N Expansion of e.g.f. arcsinh(x)/(1 - x).
%F E.g.f.: log(x + sqrt(1 + x^2))/(1 - x).
%F a(n) ~ n! * log(1 + sqrt(2)). - _Vaclav Kotesovec_, Dec 20 2017
%e arcsinh(x)/(1 - x) = x/1! + 2*x^2/2! + 5*x^3/3! + 20*x^4/4! + 109*x^5/5! + ...
%p a:=series(arcsinh(x)/(1 - x),x=0,24): seq(n!*coeff(a,x,n),n=0..23); # _Paolo P. Lava_, Mar 27 2019
%t nmax = 23; CoefficientList[Series[ArcSinh[x]/(1 - x), {x, 0, nmax}], x] Range[0, nmax]!
%t nmax = 23; CoefficientList[Series[Log[x + Sqrt[1 + x^2]]/(1 - x), {x, 0, nmax}], x] Range[0, nmax]!
%o (PARI) first(n) = x='x+O('x^n); Vec(serlaplace(asinh(x)/(1 - x)), -n) \\ _Iain Fox_, Dec 19 2017
%Y Cf. A001818, A009628, A081358, A186763, A281964, A296726.
%K nonn
%O 0,3
%A _Ilya Gutkovskiy_, Dec 19 2017
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