A012575 tan(arcsinh(x)*log(x+1))=2/2!*x^2-3/3!*x^3+4/4!*x^4-20/5!*x^5...

0, 0, 2, -3, 4, -20, 398, -3339, 20424, -170064, 2564442, -36806715, 452112780, -6050016180, 103580488230, -1918670093235, 34463159406480, -644382830011200, 13519192507361970, -305019253676537235

Offset

0,3

Links

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

Formula

a(n) ~ n! / ((Pi/(2*(1+r)*log(1+r)) + log(1+r)/sqrt(1+r^2)) * r^(n+1)), where r = -0.865492354980428358034918717204144097599568833... is the root of the equation arcsinh(r)*log(1+r) = Pi/2. - Vaclav Kotesovec, Feb 02 2015

Mathematica

CoefficientList[Series[Tan[ArcSinh[x]*Log[1 + x]], {x, 0, 20}], x] * Range[0, 20]! (* Vaclav Kotesovec, Feb 02 2015 *)

Crossrefs

Sequence in context: A012574 A012282 A012287 * A012580 A246391 A303973

Adjacent sequences: A012572 A012573 A012574 * A012576 A012577 A012578

Keyword

sign

Author

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

Extensions

Prepended missing a(0)=0 and a(1)=0 from Vaclav Kotesovec, Feb 02 2015

Status

approved