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%I #4 Dec 27 2017 15:20:52
%S 1,-1,-4,-7,1003,64836,3350349,104475395,-12291888052,-4268687337603,
%T -877769324284177,-139938933307889412,-9581950082738688167,
%U 6333750977985105075527,4837035706491587870342140,2439859866050865745230242689,1033093869484852949078289394195
%N Expansion of e.g.f. exp(cos(tan(x))-1) (even powers only).
%F a(n) = (2*n)! * [x^(2*n)] exp(cos(tan(x))-1).
%e exp(cos(tan(x))-1) = 1 - x^2/2! - 4*x^4/4! - 7*x^6/6! + 1003*x^8/8! + 64836*x^10/10! + ...
%t nmax = 16; Table[(CoefficientList[Series[Exp[Cos[Tan[x]] - 1], {x, 0, 2 nmax}], x] Range[0, 2 nmax]!)[[n]], {n, 1, 2 nmax + 1, 2}]
%Y Cf. A003710, A009074, A009201, A009202, A009203, A009204, A009238, A009239, A009240, A009241, A009254, A297214.
%K sign
%O 0,3
%A _Ilya Gutkovskiy_, Dec 27 2017
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