A013290 Expansion of e.g.f. arctanh(log(x+1) - tanh(x)).

0, 0, -1, 4, -6, 8, -150, 1832, -16520, 134752, -1214640, 15556352, -248089248, 3892532096, -58976309392, 950047701696, -17523231473280, 360338416640512, -7742581556059008, 169950515543962112, -3892670273719159040, 95372338941501045760

Offset

0,4

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..200

Example

-(1/2!)*x^2 + (4/3!)*x^3 - (6/4!)*x^4 + (8/5!)*x^5 - ...

Mathematica

Range[0, 25]! CoefficientList[Series[ArcTanh[Log[x + 1] - Tanh[x]], {x, 0, 25}], x] (* Vincenzo Librandi, Aug 03 2018 *)

Prog

(Magma) m:=30; R<x>:=PowerSeriesRing(Rationals(), m); b:=Coefficients(R!(1+Argtanh(Log(x+1) - Tanh(x)))); [0] cat [Factorial(n-1)*b[n]: n in [2..m]]; // Vincenzo Librandi, Aug 03 2018

Crossrefs

Sequence in context: A013287 A013283 A013284 * A095211 A141569 A200621

Adjacent sequences: A013287 A013288 A013289 * A013291 A013292 A013293

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 03 2018

Status

approved