login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A012291 Expansion of e.g.f. arcsinh(sin(x)*exp(x)). 1

%I

%S 0,1,2,1,-12,-75,-98,3141,37128,79145,-4068838,-70096919,-208084932,

%T 14605150365,331136373622,1267818101421,-111869011278192,

%U -3149733764010415,-14850194074608718,1567505717936558161

%N Expansion of e.g.f. arcsinh(sin(x)*exp(x)).

%H G. C. Greubel, <a href="/A012291/b012291.txt">Table of n, a(n) for n = 0..423</a>

%e E.g.f. = x + 2*x^2/2! + x^3/3! - 12*x^4/4! - 75*x^5/5! + ...

%e Lim sup n->infinity (|a(n)|/n!)^(1/n) = 1.464319877618... = abs(1/r), where r is the complex root of the equation exp(2*r)*(sin(r))^2 = -1. - _Vaclav Kotesovec_, Nov 02 2013

%t CoefficientList[Series[ArcSinh[Sin[x]*Exp[x]], {x, 0, 20}], x]* Range[0, 20]! (* _Vaclav Kotesovec_, Oct 30 2013 *)

%o (PARI) x='x+O('x^30); concat([0], Vec(serlaplace(asinh(sin(x)*exp(x))))) \\ _G. C. Greubel_, Oct 26 2018

%o (MAGMA) m:=30; R<x>:=PowerSeriesRing(Rationals(), m); b:=Coefficients(R!( Argsinh(Sin(x)*Exp(x)) )); [0] cat [Factorial(n)*b[n]: n in [1..m-1]]; // _G. C. Greubel_, Oct 26 2018

%K sign

%O 0,3

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

%E Prepended missing a(0)=0 from _Vaclav Kotesovec_, Nov 02 2013

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 July 14 09:22 EDT 2020. Contains 335720 sequences. (Running on oeis4.)