A012263 Expansion of e.g.f. exp(arctanh(arctanh(x))).

1, 1, 1, 5, 17, 129, 769, 7797, 66849, 848481, 9506241, 145041093, 2007271089, 35799178401, 589807203777, 12045448529397, 230194642564161, 5298881528389185, 115219444193968257, 2952169020073027845

Offset: 0

Author

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

Keywords

• nonn

Examples

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

Links

• G. C. Greubel, Table of n, a(n) for n = 0..430

Programs

Magma

m:=30; R:=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

Maple

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

Mathematica

With[{nn=30},CoefficientList[Series[Exp[ArcTanh[ArcTanh[x]]],{x,0,nn}],x] Range[0,nn]!] (* Ray Chandler, Nov 28 2016 *)

PARI

x='x+O('x^30); Vec(serlaplace(exp(atanh(atanh(x))))) \\ G. C. Greubel, Oct 28 2018