A012285 Expansion of e.g.f. arcsinh(sin(x)*log(x+1)).

0, 0, 2, -3, 4, -20, -10, 609, -3880, 32040, -110822, -2853235, 62173340, -984765132, 13116545598, -105359946615, -269704385808, 34712027932816, -1001624343871182, 18826756309101213, -210544812030819596

Offset

0,3

Links

G. C. Greubel, Table of n, a(n) for n = 0..440

Formula

Lim sup n->infinity (|a(n)|/n!)^(1/n) = 1.144501665199369... = abs(1/r), where r is the complex root of the equation 1+r = exp(-I/sin(r)). - Vaclav Kotesovec, Nov 02 2013

Example

E.g.f. = 2*x^2/2! - 3*x^3/3! + 4*x^4/4! - 20*x^5/5! + ...

Mathematica

CoefficientList[Series[ArcSinh[Sin[x]*Log[x+1]], {x, 0, 20}], x]* Range[0, 20]! (* Vaclav Kotesovec, Oct 30 2013 *)

Prog

(PARI) x='x+O('x^30); concat([0, 0], Vec(serlaplace(asinh(sin(x)* log(x+1))))) \\ G. C. Greubel, Oct 26 2018
(Magma) m:=30; R<x>:=PowerSeriesRing(Rationals(), m); b:=Coefficients(R!( Argsinh(Sin(x)*Log(x+1)) )); [0, 0] cat [Factorial(n+1)*b[n]: n in [1..m-2]]; // G. C. Greubel, Oct 26 2018

Crossrefs

Sequence in context: A276105 A247574 A169901 * A012281 A098503 A092974

Adjacent sequences: A012282 A012283 A012284 * A012286 A012287 A012288

Keyword

sign

Author

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

Extensions

Prepended missing a(0)=0, a(1)=0 from Vaclav Kotesovec, Nov 02 2013

Status

approved