A009438 -id:A009438 - cp's OEIS frontend

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

R. H. Hardin

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

Cf. A009405 - A009420, A009422 - A009438.

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

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

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

Extended with signs by Olivier Gérard, Mar 15 1997

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

A009437 Expansion of e.g.f. log(1+x)/exp(sinh(x)).

Original entry on oeis.org

0, 1, -3, 8, -28, 119, -581, 3345, -22352, 170889, -1480881, 14361885, -154177068, 1814792589, -23230500541, 321160966833, -4767464107904, 75612375796689, -1275789176648193, 22815192314465685, -431023517858496044

Offset: 0

R. H. Hardin

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

Cf. A009405 - A009420, A009422 - A009436, A009438, A009439.

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

With[{nn=20},CoefficientList[Series[Log[1+x]/Exp[Sinh[x]],{x,0,nn}],x] Range[0,nn]!] (* Harvey P. Dale, Oct 01 2013 *)

def A009437_list(prec):
    P. = PowerSeriesRing(QQ, prec)
    return P( log(1+x)*exp(-sinh(x)) ).egf_to_ogf().list()
A009437_list(31) # G. C. Greubel, Sep 08 2023

a(n) ~ (n-1)! * (-1)^(n+1) * exp(sinh(1)). - Vaclav Kotesovec, Jan 23 2015

Extended with signs by Olivier Gérard, Mar 15 1997

Definition clarified by Harvey P. Dale, Oct 01 2013

cp's OEIS Frontend

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

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