A013572 Expansion of e.g.f. of exp(arcsinh(x)/exp(x)).

1, 1, -1, -3, 9, 25, -145, -539, 3857, 30129, -192673, -2816979, 17218201, 364417417, -2297788337, -63429766763, 417350455329, 14529736975457, -99514205291841, -4252720982041379, 30285000226110761

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