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Expansion of e.g.f.: tanh(sin(x)*log(x+1)).
1

%I #14 Sep 08 2022 08:44:38

%S 0,0,2,-3,4,-20,-130,1869,-12280,100080,-604742,-829675,62508620,

%T -1158921972,17643171702,-190494456075,1197368304912,8324510449216,

%U -571700218304142,14677422922560141,-268070215275170156,3735756713394119820,-25728057443748879250

%N Expansion of e.g.f.: tanh(sin(x)*log(x+1)).

%H G. C. Greubel, <a href="/A012286/b012286.txt">Table of n, a(n) for n = 0..450</a>

%e E.g.f. = 2*x^2/2! - 3*x^3/3! + 4*x^4/4! - 20*x^5/5! + ...

%t With[{nn=30},CoefficientList[Series[Tanh[Sin[x]Log[x+1]],{x,0,nn}],x] Range[ 0,nn]!] (* _Harvey P. Dale_, May 06 2013 *)

%o (PARI) x='x+O('x^30); concat([0,0], Vec(serlaplace(tanh(sin(x)* log(x+1))))) \\ _G. C. Greubel_, Oct 26 2018

%o (Magma) m:=30; R<x>:=PowerSeriesRing(Rationals(), m); b:=Coefficients(R!( Tanh(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 Definition clarified by and more terms from _Harvey P. Dale_, May 06 2013