A009436 -id:A009436 - cp's OEIS frontend

A009435 Expansion of e.g.f.: log(1+x)/cosh(x).

0, 1, -1, -1, 0, 29, -105, 139, -2072, 31737, -247545, 1824151, -22456104, 313750293, -3929185169, 51584719523, -793292190480, 13137192234225, -221862616530705, 3947317975733039, -75492532592047280, 1522475446731094285

Offset: 0

R. H. Hardin

G. C. Greubel, Table of n, a(n) for n = 0..449

Cf. A009405 - A009420, A009422 - A009434, A009436 - A009439.

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

With[{nn=30},CoefficientList[Series[Log[1+x]/Cosh[x],{x,0,nn}],x] Range[ 0,nn]!] (* Harvey P. Dale, Oct 01 2014 *)

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

def A009435_list(prec):
    P. = PowerSeriesRing(QQ, prec)
    return P( log(1+x)/cosh(x) ).egf_to_ogf().list()
A009435_list(40) # G. C. Greubel, Sep 06 2023

a(n) ~ (-1)^(n+1) * (n-1)! / cosh(1). - Vaclav Kotesovec, Oct 01 2014

Extended with signs by Olivier Gérard, Mar 15 1997

Definition clarified and prior Mathematica program replaced by Harvey P. Dale, Oct 01 2014

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

A009435 Expansion of e.g.f.: log(1+x)/cosh(x).

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