OFFSET
0,4
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..422 (terms 0..200 from Alois P. Heinz)
FORMULA
a(n) ~ (n-1)! / (2*(exp(r)-1)^n), where r = 0.5122224330332299... is the root of the equation r*exp(exp(r)-1)=1. - Vaclav Kotesovec, Oct 24 2013
EXAMPLE
arctanh(exp(x)*log(x+1)) = x+1/2!*x^2+4/3!*x^3+12/4!*x^4+103/5!*x^5...
MAPLE
seq(coeff(series(factorial(n)*arctanh(exp(x)*log(x+1)), x, n+1), x, n), n = 0 .. 22); # Muniru A Asiru, Oct 28 2018
MATHEMATICA
CoefficientList[Series[ArcTanh[Exp[x]*Log[x + 1]], {x, 0, 20}], x]*
Range[0, 20]! (* Bruno Berselli, Feb 17 2013 *)
PROG
(PARI) x='x+O('x^30); concat([0], Vec(serlaplace(atanh(exp(x)* log(x+1))))) \\ G. C. Greubel, Oct 28 2018
(Magma) m:=30; R<x>:=PowerSeriesRing(Rationals(), m); b:=Coefficients(R!( Argtanh(Exp(x)*Log(x+1)) )); [0] cat [Factorial(n)*b[n]: n in [1..m-1]]; // G. C. Greubel, Oct 28 2018
CROSSREFS
KEYWORD
nonn
AUTHOR
Patrick Demichel (patrick.demichel(AT)hp.com)
EXTENSIONS
Prepended a(0)=0 by Bruno Berselli, Feb 17 2013
STATUS
approved