A009427 Expansion of e.g.f. log(1+x)/cos(tan(x)).

0, 1, -1, 5, -12, 109, -405, 4913, -24976, 372633, -2419425, 42646845, -338219244, 6863821509, -64452230661, 1478191260393, -16062969072000, 410493211996977, -5072547848554017, 142840036992492789, -1979718755185227180

Offset: 0

Author

R. H. Hardin

Keywords

• sign
• easy

Links

• Vaclav Kotesovec, Table of n, a(n) for n = 0..446
• Vaclav Kotesovec, Graph - asymptotic ratio

Crossrefs

Cf. A009405 - A009420, A009422 - A009426, A009428 - A009439.

Programs

Magma

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

Mathematica

With[{m=25}, CoefficientList[Series[Log[1+x]/Cos[Tan[x]], {x,0,m}], x]*Range[0, m]!] (* modified by G. C. Greubel, Sep 06 2023 *)
CoefficientList[Series[Log[1 + x]*Sec[Tan[x]], {x, 0, 20}], x] * Range[0, 20]! (* Vaclav Kotesovec, Jan 24 2015 *)

PARI

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

SageMath

def A009427_list(prec):
    P. = PowerSeriesRing(QQ, prec)
    return P( log(1+x)/cos(tan(x)) ).egf_to_ogf().list()
A009427_list(40) # G. C. Greubel, Sep 06 2023

Formula

a(n) ~ (n-1)! * (-1)^(n+1) / cos(tan(1)) * (1 + tan(tan(1)) / ((cos(1))^2*n)). - Vaclav Kotesovec, Jan 27 2015

Extensions

Extended with signs by Olivier Gérard, Mar 15 1997