A012291 Expansion of e.g.f. arcsinh(sin(x)*exp(x)).

0, 1, 2, 1, -12, -75, -98, 3141, 37128, 79145, -4068838, -70096919, -208084932, 14605150365, 331136373622, 1267818101421, -111869011278192, -3149733764010415, -14850194074608718, 1567505717936558161

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