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

0,6

Links

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

Formula

a(n) ~ (n-1)! * (-1)^(n+1) / cosh(tan(1)). - Vaclav Kotesovec, Jan 23 2015

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 *)

Prog

(Magma)
R<x>:=PowerSeriesRing(Rationals(), 30);
[0] cat Coefficients(R!(Laplace( Log(1+x)/Cosh(Tan(x)) ))); // G. C. Greubel, Sep 06 2023
(SageMath)
def A009433_list(prec):
    P.<x> = PowerSeriesRing(QQ, prec)
    return P( log(1+x)/cosh(tan(x)) ).egf_to_ogf().list()
A009433_list(40) # G. C. Greubel, Sep 06 2023
(PARI)  my(x='x+O('x^30)); concat([0], Vec(serlaplace(log(1+x)/cosh(tan(x))))) \\ Joerg Arndt, Sep 06 2023

Crossrefs

Cf. A009405 - A009420, A009422 - A009432, A009434 - A009439.

Sequence in context: A214863 A094766 A009407 * A275242 A030099 A085597

Adjacent sequences: A009430 A009431 A009432 * A009434 A009435 A009436

Keyword

sign,easy

Author

R. H. Hardin

Extensions

Extended with signs by Olivier Gérard, Mar 15 1997

Status

approved