login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A012262 Expansion of e.g.f. exp(arctanh(arcsinh(x))). 1
1, 1, 1, 2, 5, 24, 109, 552, 3177, 28032, 227961, 1778688, 15773229, 212383872, 2521786149, 25215328512, 294715261521, 5734229114880, 91106569198449, 1029078328135680, 14283819393505749, 410202091438571520 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,4

COMMENTS

a(32) is negative. - Vaclav Kotesovec, Oct 25 2013

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..200

FORMULA

a(n) ~ 8*n^(n-1)*(2*sin(Pi*n/2)-Pi*cos(Pi*n/2))/((4+Pi^2)^(3/2)*exp(n)). - Vaclav Kotesovec, Oct 25 2013

EXAMPLE

E.g.f. = 1 + x + x^2/2! + 2*x^3/3! + 5*x^4/4! + 24*x^5/5! + ...

MAPLE

seq(coeff(series(factorial(n)*exp(arctanh(arcsinh(x))), x, n+1), x, n), n = 0 .. 25); # Muniru A Asiru, Oct 29 2018

MATHEMATICA

CoefficientList[Series[Exp[ArcTanh[ArcSinh[x]]], {x, 0, 35}], x]* Range[0, 35]! (* Vaclav Kotesovec, Oct 25 2013 *)

PROG

(PARI) x='x+O('x^30); Vec(serlaplace(exp(atanh(asinh(x))))) \\ G. C. Greubel, Oct 28 2018

(MAGMA) m:=30; R<x>:=PowerSeriesRing(Rationals(), m); b:=Coefficients(R!( Exp(Argtanh(Argsinh(x))) )); [Factorial(n-1)*b[n]: n in [1..m-1]]; // G. C. Greubel, Oct 28 2018

CROSSREFS

Sequence in context: A200402 A010365 A218939 * A012254 A322897 A284230

Adjacent sequences:  A012259 A012260 A012261 * A012263 A012264 A012265

KEYWORD

sign

AUTHOR

Patrick Demichel (patrick.demichel(AT)hp.com)

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified May 26 04:46 EDT 2019. Contains 323579 sequences. (Running on oeis4.)