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%I #12 Sep 08 2022 08:44:38
%S 0,0,2,-3,4,-20,-10,609,-3880,32040,-110822,-2853235,62173340,
%T -984765132,13116545598,-105359946615,-269704385808,34712027932816,
%U -1001624343871182,18826756309101213,-210544812030819596
%N Expansion of e.g.f. arcsinh(sin(x)*log(x+1)).
%H G. C. Greubel, <a href="/A012285/b012285.txt">Table of n, a(n) for n = 0..440</a>
%F Lim sup n->infinity (|a(n)|/n!)^(1/n) = 1.144501665199369... = abs(1/r), where r is the complex root of the equation 1+r = exp(-I/sin(r)). - _Vaclav Kotesovec_, Nov 02 2013
%e E.g.f. = 2*x^2/2! - 3*x^3/3! + 4*x^4/4! - 20*x^5/5! + ...
%t CoefficientList[Series[ArcSinh[Sin[x]*Log[x+1]], {x, 0, 20}], x]* Range[0, 20]! (* _Vaclav Kotesovec_, Oct 30 2013 *)
%o (PARI) x='x+O('x^30); concat([0,0], Vec(serlaplace(asinh(sin(x)* log(x+1))))) \\ _G. C. Greubel_, Oct 26 2018
%o (Magma) m:=30; R<x>:=PowerSeriesRing(Rationals(), m); b:=Coefficients(R!( Argsinh(Sin(x)*Log(x+1)) )); [0,0] cat [Factorial(n+1)*b[n]: n in [1..m-2]]; // _G. C. Greubel_, Oct 26 2018
%K sign
%O 0,3
%A Patrick Demichel (patrick.demichel(AT)hp.com)
%E Prepended missing a(0)=0, a(1)=0 from _Vaclav Kotesovec_, Nov 02 2013
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