OFFSET
0,3
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..440
FORMULA
Lim sup n->infinity (|a(n)|/n!)^(1/n) = 1.144501665199369... = abs(1/r), where r is the complex root of the equation 1+r = exp(-I/sin(r)). - Vaclav Kotesovec, Nov 02 2013
EXAMPLE
E.g.f. = 2*x^2/2! - 3*x^3/3! + 4*x^4/4! - 20*x^5/5! + ...
MATHEMATICA
CoefficientList[Series[ArcSinh[Sin[x]*Log[x+1]], {x, 0, 20}], x]* Range[0, 20]! (* Vaclav Kotesovec, Oct 30 2013 *)
PROG
(PARI) x='x+O('x^30); concat([0, 0], Vec(serlaplace(asinh(sin(x)* log(x+1))))) \\ G. C. Greubel, Oct 26 2018
(Magma) m:=30; R<x>:=PowerSeriesRing(Rationals(), m); b:=Coefficients(R!( Argsinh(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)=0, a(1)=0 from Vaclav Kotesovec, Nov 02 2013
STATUS
approved