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%I #12 Dec 21 2017 06:52:05
%S 0,1,-1,1,-2,13,-64,173,-720,12409,-114816,370137,-1491456,88556037,
%T -1263184896,2668274373,21448022016,2491377242481,-50233550831616,
%U -34526890553679,5153298175033344,202383113207336829,-5453228045913292800,-25792743610973373219,1393299559788718325760
%N Expansion of e.g.f. log(1 + arcsinh(x)).
%H Robert Israel, <a href="/A296435/b296435.txt">Table of n, a(n) for n = 0..451</a>
%F E.g.f.: log(1 + log(x + sqrt(1 + x^2))).
%F a(n) ~ 4*(Pi*cos(Pi*n/2) + 2*sin(Pi*n/2)) * n^(n-1) / ((4 + Pi^2) * exp(n)). - _Vaclav Kotesovec_, Dec 21 2017
%e E.g.f.: A(x) = x/1! - x^2/2! + x^3/3! - 2*x^4/4! + 13*x^5/5! - 64*x^6/6! + ...
%p S:= series(ln(1+arcsinh(x)),x,51):
%p seq(coeff(S,x,j)*j!,j=0..50); # _Robert Israel_, Dec 12 2017
%t nmax = 24; CoefficientList[Series[Log[1 + ArcSinh[x]], {x, 0, nmax}], x] Range[0, nmax]!
%t nmax = 24; CoefficientList[Series[Log[1 + Log[x + Sqrt[1 + x^2]]], {x, 0, nmax}], x] Range[0, nmax]!
%o (PARI) Vecrev(Pol(serlaplace(log(1 + asinh(x + O(x^30)))))) \\ _Andrew Howroyd_, Dec 12 2017
%Y Cf. A001818, A003704, A110708, A189815, A202139, A296437.
%K sign
%O 0,5
%A _Ilya Gutkovskiy_, Dec 12 2017
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