A013562 E.g.f. arcsin(log(x+1)/exp(x)).

0, 1, -3, 9, -42, 313, -3025, 35091, -482468, 7704257, -139729063, 2834494245, -63612631742, 1564879314945, -41866671551549, 1210176423684151, -37583615159233544, 1248017801182054753, -44124684998406215691

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

Sequence in context: A105804 A009402 A009584 * A081681 A281940 A141774

Adjacent sequences: A013559 A013560 A013561 * A013563 A013564 A013565

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