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%I #19 Sep 08 2022 08:44:37
%S 1,0,2,-3,23,-90,676,-4305,37533,-325332,3366166,-36472095,443702291,
%T -5732993838,80707226328,-1207617980205,19365202513145,
%U -328878787017000,5925189947339626,-112532916285619515,2251485624038961615
%N Expansion of e.g.f. cosh(log(1+x))/cos(x).
%H G. C. Greubel, <a href="/A009130/b009130.txt">Table of n, a(n) for n = 0..250</a>
%F a(n) ~ n! * (-1)^n * sin(1) / sin(2). - _Vaclav Kotesovec_, Jan 22 2015
%t CoefficientList[Series[((1 + (1 + x)^2)*Sec[x])/(2*(1 + x)), {x, 0, 20}], x] * Range[0, 20]! (* _Vaclav Kotesovec_, Jan 22 2015 *)
%t With[{nn=20},CoefficientList[Series[Cosh[Log[1+x]]/Cos[x],{x,0,nn}],x] Range[ 0,nn]!] (* _Harvey P. Dale_, Aug 21 2021 *)
%o (PARI) x='x+O('x^30); Vec(serlaplace(cosh(log(1+x))/cos(x))) \\ _G. C. Greubel_, Jul 28 2018
%o (Magma) m:=30; R<x>:=PowerSeriesRing(Rationals(), m); b:=Coefficients(R!(Cosh(Log(1+x))/Cos(x))); [Factorial(n-1)*b[n]: n in [1..m]]; // _G. C. Greubel_, Jul 28 2018
%K sign,easy
%O 0,3
%A _R. H. Hardin_
%E Extended with signs by _Olivier Gérard_, Mar 15 1997
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