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%I #21 Sep 08 2022 08:44:37
%S 1,0,1,-3,16,-100,760,-6720,67940,-772560,9760100,-135617900,
%T 2055532400,-33748556400,596675513200,-11302050942000,228340292986000,
%U -4901379615184000,111394219174810000,-2672242230261006000
%N Expansion of 1/cos(log(1+x)).
%H Vincenzo Librandi, <a href="/A009007/b009007.txt">Table of n, a(n) for n = 0..200</a>
%F a(n) ~ n! / ((exp(Pi/2)-1) * (exp(-Pi/2)-1)^n). - _Vaclav Kotesovec_, Jan 22 2015
%p seq(coeff(series(factorial(n)*(1/cos(log(1+x))), x,n+1),x,n),n=0..20); # _Muniru A Asiru_, Jul 21 2018
%t With[{nn = 50}, CoefficientList[Series[1/Cos[Log[1 + x]], {x, 0, nn}], x] Range[0, nn]!] (* _Vincenzo Librandi_, Apr 11 2014 *)
%o (PARI) x='x+O('x^30); Vec(serlaplace(1/cos(log(1+x)))) \\ _G. C. Greubel_, Jul 21 2018
%o (Magma) m:=30; R<x>:=PowerSeriesRing(Rationals(), m); b:=Coefficients(R!(1/Cos(Log(1+x)))); [Factorial(n-1)*b[n]: n in [1..m]]; // _G. C. Greubel_, Jul 21 2018
%K sign
%O 0,4
%A _R. H. Hardin_, _Simon Plouffe_