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%I #20 Sep 08 2022 08:44:37
%S 1,0,1,-3,24,-120,990,-7140,69048,-658728,7542960,-89216160,
%T 1191378408,-16691737920,255303337016,-4111553595240,70932973452032,
%U -1287129875516672,24738396315075648,-498729120183554688
%N Expansion of e.g.f. cosh(log(1+x)/cos(x)).
%H G. C. Greubel, <a href="/A009137/b009137.txt">Table of n, a(n) for n = 0..250</a>
%F a(n) ~ (-1)^n * n! / (2 * Gamma(1/cos(1)) * n^(1 - 1/cos(1))). - _Vaclav Kotesovec_, Jul 31 2018
%p seq(coeff(series(factorial(n)*cosh(log(1+x)/cos(x)), x,n+1),x,n),n=0..20); # _Muniru A Asiru_, Jul 31 2018
%t With[{nmax = 30}, CoefficientList[Series[Cosh[Log[1 + x]/Cos[x]], {x, 0, nmax}], x]*Range[0, nmax]!] (* _G. C. Greubel_, Jul 30 2018 *)
%o (PARI) x='x+O('x^30); Vec(serlaplace(cosh(log(1+x)/cos(x)))) \\ _G. C. Greubel_, Jul 30 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 30 2018
%K sign,easy
%O 0,4
%A _R. H. Hardin_
%E Extended with signs by _Olivier Gérard_, Mar 15 1997