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Expansion of e.g.f. exp(arctanh(arctanh(x))).
2

%I #15 Sep 08 2022 08:44:38

%S 1,1,1,5,17,129,769,7797,66849,848481,9506241,145041093,2007271089,

%T 35799178401,589807203777,12045448529397,230194642564161,

%U 5298881528389185,115219444193968257,2952169020073027845

%N Expansion of e.g.f. exp(arctanh(arctanh(x))).

%H G. C. Greubel, <a href="/A012263/b012263.txt">Table of n, a(n) for n = 0..430</a>

%e E.g.f. = 1 + x + x^2/2! + 5*x^3/3! + 17*x^4/4! + 129*x^5/5! + ...

%p seq(coeff(series(factorial(n)*exp(arctanh(arctanh(x))),x,n+1), x, n), n = 0 .. 20); # _Muniru A Asiru_, Oct 28 2018

%t With[{nn=30},CoefficientList[Series[Exp[ArcTanh[ArcTanh[x]]],{x,0,nn}],x] Range[0,nn]!] (* _Ray Chandler_, Nov 28 2016 *)

%o (PARI) x='x+O('x^30); Vec(serlaplace(exp(atanh(atanh(x))))) \\ _G. C. Greubel_, Oct 28 2018

%o (Magma) m:=30; R<x>:=PowerSeriesRing(Rationals(), m); b:=Coefficients(R!( Exp(Argtanh(Argtanh(x))) )); [Factorial(n-1)*b[n]: n in [1..m-1]]; // _G. C. Greubel_, Oct 28 2018

%K nonn

%O 0,4

%A Patrick Demichel (patrick.demichel(AT)hp.com)