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%I #19 Sep 08 2022 08:44:38
%S 1,1,1,2,5,24,109,552,3177,28032,227961,1778688,15773229,212383872,
%T 2521786149,25215328512,294715261521,5734229114880,91106569198449,
%U 1029078328135680,14283819393505749,410202091438571520
%N Expansion of e.g.f. exp(arctanh(arcsinh(x))).
%C a(32) is negative. - _Vaclav Kotesovec_, Oct 25 2013
%H Alois P. Heinz, <a href="/A012262/b012262.txt">Table of n, a(n) for n = 0..200</a>
%F a(n) ~ 8*n^(n-1)*(2*sin(Pi*n/2)-Pi*cos(Pi*n/2))/((4+Pi^2)^(3/2)*exp(n)). - _Vaclav Kotesovec_, Oct 25 2013
%e E.g.f. = 1 + x + x^2/2! + 2*x^3/3! + 5*x^4/4! + 24*x^5/5! + ...
%p seq(coeff(series(factorial(n)*exp(arctanh(arcsinh(x))),x,n+1), x, n), n = 0 .. 25); # _Muniru A Asiru_, Oct 29 2018
%t CoefficientList[Series[Exp[ArcTanh[ArcSinh[x]]], {x, 0, 35}], x]* Range[0, 35]! (* _Vaclav Kotesovec_, Oct 25 2013 *)
%o (PARI) x='x+O('x^30); Vec(serlaplace(exp(atanh(asinh(x))))) \\ _G. C. Greubel_, Oct 28 2018
%o (Magma) m:=30; R<x>:=PowerSeriesRing(Rationals(), m); b:=Coefficients(R!( Exp(Argtanh(Argsinh(x))) )); [Factorial(n-1)*b[n]: n in [1..m-1]]; // _G. C. Greubel_, Oct 28 2018
%K sign
%O 0,4
%A Patrick Demichel (patrick.demichel(AT)hp.com)
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