A012260 Expansion of e.g.f. exp(arctanh(arctan(x))).

1, 1, 1, 1, 1, 9, 49, 57, -447, 5169, 78561, -93807, -5655231, 31981689, 1014069393, -3857766903, -187639949439, 1058896281825, 51144433721793, -286891166986335, -16631972691697791, 108826313005021545

Offset

0,6

Links

G. C. Greubel, Table of n, a(n) for n = 0..450

Example

E.g.f. = 1 + x + x^2/2! + x^3/3! + x^4/4! + 9*x^5/5! + ...

Maple

seq(coeff(series(factorial(n)*exp(arctanh(arctan(x))), x, n+1), x, n), n = 0 .. 25); # Muniru A Asiru, Oct 29 2018

Mathematica

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

Prog

(PARI) x='x+O('x^30); Vec(serlaplace(exp(atanh(atan(x))))) \\ G. C. Greubel, Oct 28 2018
(Magma) m:=30; R<x>:=PowerSeriesRing(Rationals(), m); b:=Coefficients(R!( Exp(Argtanh(Arctan(x))) )); [Factorial(n-1)*b[n]: n in [1..m-1]]; // G. C. Greubel, Oct 28 2018

Crossrefs

Sequence in context: A140891 A072461 A181607 * A262537 A133478 A339129

Adjacent sequences: A012257 A012258 A012259 * A012261 A012262 A012263

Keyword

sign

Author

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

Status

approved