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

0,4

Links

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

Example

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

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 *)

Prog

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

Crossrefs

Sequence in context: A256459 A113936 A365295 * A076448 A096310 A236530

Adjacent sequences: A012260 A012261 A012262 * A012264 A012265 A012266

Keyword

nonn

Author

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

Status

approved