OFFSET
0,3
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..430
FORMULA
a(n) ~ (n-1)! * (-1)^n / (2 * r^n), where r = 0.7642695126688585683463... is the root of the equation log(1-r)*sin(r) = -1. - Vaclav Kotesovec, Feb 05 2015
EXAMPLE
E.g.f. = 2*x^2/2! - 3*x^3/3! + 4*x^4/4! - 20*x^5/5! + ...
MATHEMATICA
CoefficientList[Series[ArcTanh[Log[1 + x]*Sin[x]], {x, 0, 20}], x] * Range[0, 20]! (* Vaclav Kotesovec, Feb 05 2015 *)
PROG
(PARI) x='x+O('x^30); concat([0, 0], Vec(serlaplace(atanh(sin(x)* log(x+1))))) \\ G. C. Greubel, Oct 26 2018
(Magma) m:=30; R<x>:=PowerSeriesRing(Rationals(), m); b:=Coefficients(R!( Argtanh(Sin(x)*Log(x+1)) )); [0, 0] cat [Factorial(n+1)*b[n]: n in [1..m-2]]; // G. C. Greubel, Oct 26 2018
CROSSREFS
KEYWORD
sign
AUTHOR
Patrick Demichel (patrick.demichel(AT)hp.com)
EXTENSIONS
Prepended missing a(0)=a(1)=0 from Vaclav Kotesovec, Feb 05 2015
STATUS
approved