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 A013562 E.g.f. arcsin(log(x+1)/exp(x)). 1
 0, 1, -3, 9, -42, 313, -3025, 35091, -482468, 7704257, -139729063, 2834494245, -63612631742, 1564879314945, -41866671551549, 1210176423684151, -37583615159233544, 1248017801182054753, -44124684998406215691 (list; graph; refs; listen; history; text; internal format)
 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

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Last modified August 2 21:27 EDT 2024. Contains 374875 sequences. (Running on oeis4.)