A009427 - OEIS

%I #25 Sep 06 2023 03:14:52

%S 0,1,-1,5,-12,109,-405,4913,-24976,372633,-2419425,42646845,

%T -338219244,6863821509,-64452230661,1478191260393,-16062969072000,

%U 410493211996977,-5072547848554017,142840036992492789,-1979718755185227180

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

%H Vaclav Kotesovec, <a href="/A009427/b009427.txt">Table of n, a(n) for n = 0..446</a>

%H Vaclav Kotesovec, <a href="/A009427/a009427.jpg">Graph - asymptotic ratio</a>

%F a(n) ~ (n-1)! * (-1)^(n+1) / cos(tan(1)) * (1 + tan(tan(1)) / ((cos(1))^2*n)). - _Vaclav Kotesovec_, Jan 27 2015

%t 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 *)

%t CoefficientList[Series[Log[1 + x]*Sec[Tan[x]], {x, 0, 20}], x] * Range[0, 20]! (* _Vaclav Kotesovec_, Jan 24 2015 *)

%o (Magma)

%o R<x>:=PowerSeriesRing(Rationals(), 30);

%o [0] cat Coefficients(R!(Laplace( Log(1+x)/Cos(Tan(x)) ))); // _G. C. Greubel_, Sep 06 2023

%o (SageMath)

%o def A009427_list(prec):

%o     P.<x> = PowerSeriesRing(QQ, prec)

%o     return P( log(1+x)/cos(tan(x)) ).egf_to_ogf().list()

%o A009427_list(40) # _G. C. Greubel_, Sep 06 2023

%o (PARI) my(x='x+O('x^30)); concat([0],Vec(serlaplace(log(1+x)/cos(tan(x))))) \\ _Joerg Arndt_, Sep 06 2023

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

%K sign,easy

%O 0,4

%A _R. H. Hardin_

%E Extended with signs by _Olivier Gérard_, Mar 15 1997