A009433 Expansion of e.g.f. log(1+x)/cosh(tan(x)).
0, 1, -1, -1, 0, -11, 15, 27, -504, 11817, -94185, 1226455, -12442056, 155936221, -1995562569, 27870901107, -423463160400, 6793396567633, -117302680146033, 2130615128588591, -40960288523646320, 827190717641773765
Offset: 0
Links
- G. C. Greubel, Table of n, a(n) for n = 0..448
Programs
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Magma
R
:=PowerSeriesRing(Rationals(), 30); [0] cat Coefficients(R!(Laplace( Log(1+x)/Cosh(Tan(x)) ))); // G. C. Greubel, Sep 06 2023 -
Mathematica
With[{m=25}, CoefficientList[Series[Log[1+x]/Cosh[Tan[x]], {x,0,m}], x]*Range[0, m]!] (* modified by G. C. Greubel, Sep 06 2023 *) CoefficientList[Series[Log[1 + x]*Sech[Tan[x]], {x, 0, 20}], x] * Range[0, 20]! (* Vaclav Kotesovec, Jan 23 2015 *) -
PARI
my(x='x+O('x^30)); concat([0],Vec(serlaplace(log(1+x)/cosh(tan(x))))) \\ Joerg Arndt, Sep 06 2023 -
SageMath
def A009433_list(prec): P.
= PowerSeriesRing(QQ, prec) return P( log(1+x)/cosh(tan(x)) ).egf_to_ogf().list() A009433_list(40) # G. C. Greubel, Sep 06 2023
Formula
a(n) ~ (n-1)! * (-1)^(n+1) / cosh(tan(1)). - Vaclav Kotesovec, Jan 23 2015
Extensions
Extended with signs by Olivier Gérard, Mar 15 1997