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%I #19 Mar 08 2023 12:08:39
%S 1,0,1,-3,20,-120,976,-8568,88640,-1011840,12933376,-180964608,
%T 2767631360,-45799004160,816582578176,-15594628021248,317710534983680,
%U -6876762625966080,157606194409701376,-3812723805066559488
%N Expansion of e.g.f. cosh(log(1+tan(x))).
%H G. C. Greubel, <a href="/A009125/b009125.txt">Table of n, a(n) for n = 0..250</a>
%F E.g.f.: cosh(log(1+tan(x))).
%F a(n) ~ n! * (-1)^n * 4^n / Pi^(n+1). - _Vaclav Kotesovec_, Jan 22 2015
%t CoefficientList[Series[(1 + (1 + Tan[x])^2)/(2*(1 + Tan[x])), {x, 0, 20}], x] * Range[0, 20]! (* _Vaclav Kotesovec_, Jan 22 2015 *)
%o (PARI) x='x+O('x^30); Vec(serlaplace(cosh(log(1+tan(x))))) \\ _G. C. Greubel_, Jul 28 2018
%o (Magma) m:=30; R<x>:=PowerSeriesRing(Rationals(), m); b:=Coefficients(R!(Cosh(Log(1+Tan(x))))); [Factorial(n-1)*b[n]: n in [1..m]]; // _G. C. Greubel_, Jul 28 2018
%K sign,easy
%O 0,4
%A _R. H. Hardin_
%E Extended with signs by _Olivier Gérard_, Mar 15 1997
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