A009439 Expansion of e.g.f. log(1+x)/exp(tanh(x)).

0, 1, -3, 8, -16, 29, -191, 1980, -14456, 85713, -657171, 7877880, -97759608, 1100545341, -13021637695, 185198054748, -2933940050000, 46990261427073, -774002505048195, 13811029423532424, -266175983849182016

Offset: 0

Author

R. H. Hardin

Keywords

• sign
• easy

Links

• G. C. Greubel, Table of n, a(n) for n = 0..448

Crossrefs

Cf. A009405 - A009420, A009422 - A009438.

Programs

Magma

R:=PowerSeriesRing(Rationals(), 30);
[0] cat Coefficients(R!(Laplace( Log(1+x)*Exp(-Tanh(x)) ))); // G. C. Greubel, Sep 08 2023

Mathematica

With[{nn=20},CoefficientList[Series[Log[1+x]/Exp[Tanh[x]],{x,0,nn}],x] Range[0,nn]!] (* Harvey P. Dale, May 19 2023 *)

SageMath

def A009439_list(prec):
    P. = PowerSeriesRing(QQ, prec)
    return P( log(1+x)*exp(-tanh(x)) ).egf_to_ogf().list()
A009439_list(31) # G. C. Greubel, Sep 08 2023

Extensions

Extended with signs by Olivier Gérard, Mar 15 1997

Definition clarified and previous Mathematica program replaced by Harvey P. Dale, May 19 2023