A009434 Expansion of e.g.f: log(1+x)/cosh(tanh(x)).

0, 1, -1, -1, 0, 69, -225, -1653, 3976, 187401, -965385, -14516745, 61266744, 3032650893, -21187300953, -491788726653, 2947006495920, 166337505847057, -1463633608132017, -46261934493321105, 358635306874354320

Offset: 0

Author

R. H. Hardin

Keywords

• sign
• easy

Links

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

Crossrefs

Cf. A009405 - A009420, A009422 - A009433, A009435 - A009439.

Programs

Magma

R:=PowerSeriesRing(Rationals(), 30);
[0] cat Coefficients(R!(Laplace( Log(1+x)/Cosh(Tanh(x)) ))); // G. C. Greubel, Sep 06 2023

Mathematica

With[{nn=20},CoefficientList[Series[Log[1+x]/Cosh[Tanh[x]],{x,0,nn}], x] Range[0,nn]!] (* Harvey P. Dale, Jun 19 2013 *)

PARI

my(x='x+O('x^30)); concat([0],Vec(serlaplace(log(1+x)/cosh(tanh(x))))) \\ Joerg Arndt, Sep 06 2023

SageMath

def A009434_list(prec):
    P. = PowerSeriesRing(QQ, prec)
    return P( log(1+x)/cosh(tanh(x)) ).egf_to_ogf().list()
A009434_list(40) # G. C. Greubel, Sep 06 2023

Extensions

Extended with signs by Olivier Gérard, Mar 15 1997

Definition clarified and prior Mathematica program replaced by Harvey P. Dale, Jun 19 2013