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A012302
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Expansion of e.g.f. sec(sin(x)*sin(x)), even powers only.
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1
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1, 0, 12, -240, 12432, -1073280, 125898432, -20938794240, 4567638266112, -1267670125547520, 437480763704527872, -183445824359628779520, 91908363767795383898112, -54223577318067990113648640
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OFFSET
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0,3
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LINKS
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FORMULA
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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
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EXAMPLE
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sec(sin(x)*sin(x)) = 1 + 12/4!*x^4 - 240/6!*x^6 + 12432/8!*x^8 + ...
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MAPLE
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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
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MATHEMATICA
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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 *)
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PROG
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(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
(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
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CROSSREFS
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KEYWORD
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sign
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AUTHOR
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Patrick Demichel (patrick.demichel(AT)hp.com)
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STATUS
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approved
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