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%I #20 Sep 08 2022 08:44:37
%S 1,0,-2,3,1,-30,164,-525,-391,22428,-206686,1039995,1161337,-96216978,
%T 1241356024,-8517557685,-12681799919,1373978443800,-22791296600794,
%U 198084321525267,368659923645521,-49339565916861990
%N Expansion of e.g.f. cos(x)/cosh(log(1+x)).
%H G. C. Greubel, <a href="/A009108/b009108.txt">Table of n, a(n) for n = 0..250</a>
%F a(n) ~ n! * (exp(-1) * sin(1 + (3*n+1)*Pi/4) - exp(1) * sin(1 - (3*n+1)*Pi/4)) / 2^((n+1)/2). - _Vaclav Kotesovec_, Jul 28 2018
%F a(n)+a(n+2*p) is divisible by p for any prime p. - _Mark van Hoeij_, Jun 13 2019
%t With[{nmax = 30}, CoefficientList[Series[Cos[x]/Cosh[Log[1 + x]], {x, 0, nmax}], x]*Range[0, nmax]!] (* _G. C. Greubel_, Jul 26 2018 *)
%o (PARI) x='x+O('x^30); Vec(serlaplace(cos(x)/cosh(log(1+x)))) \\ _G. C. Greubel_, Jul 26 2018
%o (Magma) m:=30; R<x>:=PowerSeriesRing(Rationals(), m); b:=Coefficients(R!(Cos(x)/Cosh(Log(1+x)))); [Factorial(n-1)*b[n]: n in [1..m]]; // _G. C. Greubel_, Jul 26 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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