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%I #12 Sep 08 2022 08:44:38
%S 0,1,0,-1,-4,5,60,-61,-2504,-8695,100920,873479,-6889804,-142058995,
%T -4843020,19728547019,98903242096,-3531831462895,-49401992303760,
%U 493517141932559,17048746833049196,-29344831492412395,-6329111550017193300,-46994369824929657901,2170046335781374467496
%N Expansion of e.g.f. arctan(exp(x) - sec(x)).
%H Vincenzo Librandi, <a href="/A013331/b013331.txt">Table of n, a(n) for n = 0..200</a>
%e x - 1/3!*x^3 - 4/4!*x^4 + 5/5!*x^5 + 60/6!*x^6 ...
%t Range[0, 30]! CoefficientList[Series[ArcTan[Exp[x] - Sec[x]], {x, 0, 30}], x] (* _Vincenzo Librandi_, Aug 06 2018 *)
%o (Magma) m:=30; R<x>:=PowerSeriesRing(Rationals(), m); b:=Coefficients(R!(1+Arctan(Exp(x) - Sec(x)))); [0] cat [Factorial(n-1)*b[n]: n in [2..m]]; // _Vincenzo Librandi_, Aug 06 2018
%o (PARI) x = 'x + O('x^30); concat(0, Vec(serlaplace(atan(exp(x) - 1/cos(x))))) \\ _Michel Marcus_, Aug 06 2018
%K sign
%O 0,5
%A Patrick Demichel (patrick.demichel(AT)hp.com)
%E a(0)=0 inserted and title improved by _Sean A. Irvine_, Aug 05 2018
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