A012893 arcsinh(sin(x)+log(x+1)) = 2*x-1/2!*x^2-7/3!*x^3+18/4!*x^4+243/5!*x^5...

0, 2, -1, -7, 18, 243, -1785, -19086, 308980, 2736225, -90239805, -495769586, 38522052690, 39766893593, -22481798964989, 111035038388104, 16941789968380680, -219516343596465735, -15750892172912678361

Offset

0,2

Links

Table of n, a(n) for n=0..18.

Formula

Lim sup n->infinity (|a(n)|/n!)^(1/n) = 2.0027513568... = abs(1/r), where r is the complex root of the equation (r+1)*exp(sin(r)) = exp(I). - Vaclav Kotesovec, Nov 02 2013

Mathematica

CoefficientList[Series[ArcSinh[Sin[x]+Log[x+1]], {x, 0, 20}], x]* Range[0, 20]! (* Vaclav Kotesovec, Nov 01 2013 *)

Crossrefs

Sequence in context: A178622 A013070 A012888 * A013075 A009281 A141516

Adjacent sequences: A012890 A012891 A012892 * A012894 A012895 A012896

Keyword

sign

Author

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

Extensions

Prepended missing a(0)=0 from Vaclav Kotesovec, Nov 01 2013

Status

approved