A013273 Expansion of e.g.f. arctan(log(x+1) - arcsinh(x)).

0, 0, -1, 3, -6, 15, -90, 315, 2520, -42525, 332640, -3170475, 43659000, -387161775, -469188720, 61992505575, -1117425909600, 23419417796775, -552570387969600, 9277455340778625, -88132216543371000, 248023194743449125, 11316131820700106400, -844433846165173589325

Offset

0,4

Links

Stefano Spezia, Table of n, a(n) for n = 0..400

Example

-(1/2!)*x^2 + (3/3!)*x^3 - (6/4!)*x^4 + (15/5!)*x^5 - ...

Mathematica

CoefficientList[Series[ArcTan[Log[x+1] - ArcSinh[x]], {x, 0, 23}], x]Table[n!, {n, 0, 23}] (* Stefano Spezia, Jul 18 2022 *)
With[{nn=30}, CoefficientList[Series[ArcTan[Log[x+1]-ArcSinh[x]], {x, 0, nn}], x] Range[ 0, nn]!] (* Harvey P. Dale, Nov 03 2022 *)

Prog

(PARI) my(x = 'x + O('x^30)); concat([0, 0], Vec(serlaplace(atan(log(x+1) - asinh(x))))) \\ Michel Marcus, Aug 03 2018

Crossrefs

Sequence in context: A208662 A102936 A009192 * A013277 A190187 A144549

Adjacent sequences: A013270 A013271 A013272 * A013274 A013275 A013276

Keyword

sign

Author

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

Extensions

a(0)=a(1)=0 inserted and title improved by Sean A. Irvine, Aug 02 2018

More terms from Stefano Spezia, Jul 18 2022

Status

approved