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A091912
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Numerators of Taylor series for log(tan(x)+1/cos(x)).
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4
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1, 1, 1, 61, 277, 50521, 41581, 199360981, 228135437, 2404879675441, 14814847529501, 69348874393137901, 238685140977801337, 4087072509293123892361, 454540704683713199807, 441543893249023104553682821, 2088463430347521052196056349
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OFFSET
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0,4
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COMMENTS
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Absolute values of (reduced) numerators of Taylor series for the Gudermannian function gd(x)= 2*arctan(exp(x))-Pi/2. - Tamas Kalmar-Nagy (integers(AT)kalmarnagy.com), Sep 28 2007
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LINKS
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FORMULA
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E.g.f.: sech x or gd x. - Tamas Kalmar-Nagy (integers(AT)kalmarnagy.com), Sep 28 2007
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EXAMPLE
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log(tan(x)+1/cos(x)) = x + 1/6*x^3 + 1/24*x^5 + 61/5040*x^7 + 277/72576*x^9 + ...
gd(x) = x - 1/6*x^3 + 1/24*x^5 - 61/5040*x^7 + 277/72576*x^9 + ....
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MATHEMATICA
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Series[ArcTan[Sinh[x]], {x, 0, 30}] // CoefficientList[#, x]& // DeleteCases[#, 0]& // Numerator // Abs (* Jean-François Alcover, Feb 24 2014 *)
a[ n_] := (-1)^n Numerator @ SeriesCoefficient[ Gudermannian @ x, {x, 0, 2 n + 1}]; (* Michael Somos, Feb 24 2014 *)
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PROG
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(PARI) a(n)=local(X); if(n<0, 0, X=x+O(x^(2*n+2)); numerator(polcoeff(log(tan(X)+1/cos(X)), 2*n+1)))
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CROSSREFS
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KEYWORD
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nonn,frac,easy
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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