A009433 - OEIS

%I #21 Sep 06 2023 04:32:03

%S 0,1,-1,-1,0,-11,15,27,-504,11817,-94185,1226455,-12442056,155936221,

%T -1995562569,27870901107,-423463160400,6793396567633,-117302680146033,

%U 2130615128588591,-40960288523646320,827190717641773765

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

%H G. C. Greubel, <a href="/A009433/b009433.txt">Table of n, a(n) for n = 0..448</a>

%F a(n) ~ (n-1)! * (-1)^(n+1) / cosh(tan(1)). - _Vaclav Kotesovec_, Jan 23 2015

%t 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 *)

%t CoefficientList[Series[Log[1 + x]*Sech[Tan[x]], {x, 0, 20}], x] * Range[0, 20]! (* _Vaclav Kotesovec_, Jan 23 2015 *)

%o (Magma)

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

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

%o (SageMath)

%o def A009433_list(prec):

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

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

%o A009433_list(40) # _G. C. Greubel_, Sep 06 2023

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

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

%K sign,easy

%O 0,6

%A _R. H. Hardin_

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