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%I #10 Dec 19 2017 17:05:38
%S 1,1,-7,-119,4241,216241,-16578871,-1851684743,236706675617,
%T 48609995386849,-8951725537756135,-3042019551814333463,
%U 738962020041708730673,387782426903449423831441,-116858640965630479825258519,-90328812874963081877073927719
%N Expansion of e.g.f. sec(x*cos(x)) (even powers only).
%F a(n) = (2*n)! * [x^(2*n)] sec(x*cos(x)).
%e sec(x*cos(x)) = 1 + x^2/2! - 7*x^4/4! - 119*x^6/6! + 4241*x^8/8! + ...
%t nmax = 15; Table[(CoefficientList[Series[Sec[x Cos[x]], {x, 0, 2 nmax}], x] Range[0, 2 nmax]!)[[n]], {n, 1, 2 nmax + 1, 2}]
%o (PARI) first(n) = x='x+O('x^(2*n-2)); vecextract(Vec(serlaplace(1/cos(x*cos(x)))), (4^n - 1)/3) \\ _Iain Fox_, Dec 19 2017
%Y Cf. A000364, A009008, A009009, A009010, A009011, A009015, A009016, A009446, A009447, A009633, A009634, A102072, A102075, A191512, A296728, A296729, A296730, A296740.
%K sign
%O 0,3
%A _Ilya Gutkovskiy_, Dec 19 2017
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