A013562 - OEIS

%I #20 Nov 14 2016 03:25:03

%S 0,1,-3,9,-42,313,-3025,35091,-482468,7704257,-139729063,2834494245,

%T -63612631742,1564879314945,-41866671551549,1210176423684151,

%U -37583615159233544,1248017801182054753,-44124684998406215691

%N E.g.f. arcsin(log(x+1)/exp(x)).

%H G. C. Greubel, <a href="/A013562/b013562.txt">Table of n, a(n) for n = 0..200</a>

%F 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

%e x - 3/2!*x^2 + 9/3!*x^3 - 42/4!*x^4 + 313/5!*x^5 - ...

%t With[{nn=20},CoefficientList[Series[ArcSin[Log[x+1]/Exp[x]],{x,0,nn}], x]Range[0,nn]!] (* _Harvey P. Dale_, Jun 11 2012 *)

%K sign

%O 0,3

%A Patrick Demichel (patrick.demichel(AT)hp.com), Dec 11 1996

%E Offset set to 0 by _Vaclav Kotesovec_, Feb 03 2015