%I #18 Sep 08 2022 08:44:37

%S 1,0,0,-3,11,-70,534,-4725,47753,-542988,6859084,-95298995,1444301715,

%T -23711336922,419190167434,-7939747234965,160403009819921,

%U -3442962495033400,78246246638467512,-1877007578925506787

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

%H G. C. Greubel, <a href="/A009103/b009103.txt">Table of n, a(n) for n = 0..250</a>

%F a(n) ~ n! * cos(1-exp(-Pi/2)) / ((exp(Pi/2)-1) * (exp(-Pi/2)-1)^n). - _Vaclav Kotesovec_, Jan 22 2015

%t CoefficientList[Series[Cos[x]*Sec[Log[1 + x]], {x, 0, 20}], x] * Range[0, 20]! (* _Vaclav Kotesovec_, Jan 22 2015 *)

%o (PARI) x='x+O('x^30); Vec(serlaplace(cos(x)/cos(log(1+x)))) \\ _G. C. Greubel_, Jul 26 2018

%o (Magma) m:=30; R<x>:=PowerSeriesRing(Rationals(), m); b:=Coefficients(R!(Cos(x)/Cos(Log(1+x)))); [Factorial(n-1)*b[n]: n in [1..m]]; // _G. C. Greubel_, Jul 26 2018

%K sign,easy

%O 0,4

%A _R. H. Hardin_

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