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 A013572 Expansion of e.g.f. of exp(arcsinh(x)/exp(x)). 1
 1, 1, -1, -3, 9, 25, -145, -539, 3857, 30129, -192673, -2816979, 17218201, 364417417, -2297788337, -63429766763, 417350455329, 14529736975457, -99514205291841, -4252720982041379, 30285000226110761 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,4 LINKS G. C. Greubel, Table of n, a(n) for n = 0..400 FORMULA E.g.f.: (x+sqrt(1+x^2))^(1/exp(x)). - Vaclav Kotesovec, Nov 01 2013 a(n) ~ 2*exp(Pi*sin(1)/2) * sin(1+n*Pi/2-Pi*cos(1)/2) * n^(n-1) / exp(n). - Vaclav Kotesovec, Nov 01 2013 EXAMPLE exp(arcsinh(x)/exp(x)) = 1 + x - 1/2!*x^2 - 3/3!*x^3 + 9/4!*x^4 + 25/5!*x^5 - .. MATHEMATICA With[{nn=30}, CoefficientList[Series[Exp[ArcSinh[x]/Exp[x]], {x, 0, nn}], x] Range[0, nn]!] (* Harvey P. Dale, Dec 19 2011 *) PROG (PARI) x='x + O('x^50); Vec(serlaplace(exp(asinh(x)/exp(x)))) \\ G. C. Greubel, Nov 20 2016 CROSSREFS Sequence in context: A120284 A074440 A006204 * A119851 A119825 A235538 Adjacent sequences:  A013569 A013570 A013571 * A013573 A013574 A013575 KEYWORD sign AUTHOR Patrick Demichel (patrick.demichel(AT)hp.com) STATUS approved

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Last modified August 3 12:47 EDT 2021. Contains 346438 sequences. (Running on oeis4.)