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%I #25 Sep 08 2022 08:44:38
%S 1,0,12,-240,12432,-1073280,125898432,-20938794240,4567638266112,
%T -1267670125547520,437480763704527872,-183445824359628779520,
%U 91908363767795383898112,-54223577318067990113648640
%N Expansion of e.g.f. sec(sin(x)*sin(x)), even powers only.
%H G. C. Greubel, <a href="/A012302/b012302.txt">Table of n, a(n) for n = 0..225</a>
%F a(n) ~ 2 * (-1)^n * (2*n)! / (sqrt(Pi*(2+Pi)) * (log(sqrt(Pi/2) + sqrt(1+Pi/2)))^(2*n+1)). - _Vaclav Kotesovec_, Feb 08 2015
%e sec(sin(x)*sin(x)) = 1 + 12/4!*x^4 - 240/6!*x^6 + 12432/8!*x^8 + ...
%p seq(coeff(series(factorial(n)*sec(sin(x)*sin(x)),x,n+1), x, n), n = 0 .. 26,2); # _Muniru A Asiru_, Oct 26 2018
%t nn = 20; Table[(CoefficientList[Series[Sec[Sin[x]^2], {x, 0, 2*nn}], x] * Range[0, 2*nn]!)[[n]], {n, 1, 2*nn+1, 2}] (* _Vaclav Kotesovec_, Feb 08 2015 *)
%o (PARI) x='x+O('x^50); v=Vec(serlaplace(1/cos(sin(x)*sin(x)))); vector(#v\2,n,v[2*n-1]) \\ _G. C. Greubel_, Apr 11 2017
%o (Magma) m:=30; R<x>:=PowerSeriesRing(Rationals(), m); b:=Coefficients(R!( 1/Cos(Sin(x)^2) )); [Factorial(2*n)*b[2*n+1]: n in [0..Floor((m-2)/2)]]; // _G. C. Greubel_, Oct 25 2018
%Y Cf. A024264.
%K sign
%O 0,3
%A Patrick Demichel (patrick.demichel(AT)hp.com)
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