OFFSET
0,3
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..200
FORMULA
a(n) ~ n! * (-1)^(n+1) * c / (n^(3/2) * r^n), where r = 0.466059131659188864998662507... is the root of the equation log(1-r) + exp(-r) = 0, c = 0.543667388388591787444659334... = sqrt((1 - exp(-t))*(t + exp(t))/(2*Pi*t)), where t = 0.627470179597516584961148... is the root of the equation exp(t)*(1 + log(t)) = 1. - Vaclav Kotesovec, Feb 03 2015, updated Mar 22 2016
EXAMPLE
x - 3/2!*x^2 + 9/3!*x^3 - 42/4!*x^4 + 313/5!*x^5 - ...
MATHEMATICA
With[{nn=20}, CoefficientList[Series[ArcSin[Log[x+1]/Exp[x]], {x, 0, nn}], x]Range[0, nn]!] (* Harvey P. Dale, Jun 11 2012 *)
CROSSREFS
KEYWORD
sign
AUTHOR
Patrick Demichel (patrick.demichel(AT)hp.com), Dec 11 1996
EXTENSIONS
Offset set to 0 by Vaclav Kotesovec, Feb 03 2015
STATUS
approved