A012470 arcsinh(cos(x)*log(x+1))=x-1/2!*x^2-2/3!*x^3+6/4!*x^4+13/5!*x^5...

0, 1, -1, -2, 6, 13, -225, 530, 8540, -65579, -650565, 13899070, -8281878, -2388363655, 18379145603, 516826612354, -11083263907560, -64702488848279, 5027641615912599, -24199820388513346

Offset

0,4

Links

Table of n, a(n) for n=0..19.

Formula

Lim sup n->infinity (|a(n)|/n!)^(1/n) = 1.25977488234489... = abs(1/r), where r is the complex root of the equation 1+r = exp(-I/cos(r)). - Vaclav Kotesovec, Nov 02 2013

Mathematica

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

Crossrefs

Sequence in context: A245010 A057243 A294130 * A266960 A056592 A349681

Adjacent sequences: A012467 A012468 A012469 * A012471 A012472 A012473

Keyword

sign

Author

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

Extensions

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

Status

approved