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
0, 1, 2, 1, -12, -75, -98, 3141, 37128, 79145, -4068838, -70096919, -208084932, 14605150365, 331136373622, 1267818101421, -111869011278192, -3149733764010415, -14850194074608718, 1567505717936558161 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

G. C. Greubel, Table of n, a(n) for n = 0..423

EXAMPLE

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

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

MATHEMATICA

CoefficientList[Series[ArcSinh[Sin[x]*Exp[x]], {x, 0, 20}], x]* Range[0, 20]! (* Vaclav Kotesovec, Oct 30 2013 *)

PROG

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

(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

CROSSREFS

Sequence in context: A012931 A013159 A012590 * A012585 A053566 A009483

Adjacent sequences:  A012288 A012289 A012290 * A012292 A012293 A012294

KEYWORD

sign

AUTHOR

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

EXTENSIONS

Prepended missing a(0)=0 from Vaclav Kotesovec, Nov 02 2013

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 June 6 18:59 EDT 2020. Contains 334832 sequences. (Running on oeis4.)