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A213067
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E.g.f.: arctan(cos(x)^2) - Pi/4.
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3
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0, -1, -2, 44, 1408, -18016, -5095232, -139605376, 56961507328, 8306292414464, -1178066937638912, -640316054325354496, -7088737339266301952, 76268423227563817631744, 18895160315230467816030208, -12297988177132848140606242816
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OFFSET
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0,3
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COMMENTS
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This function is even, with constant term Pi/4 = 0.785398163397...
It was missing from OEIS entries by Patrick Demichel.
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LINKS
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FORMULA
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E.g.f.: arctan(cos(x)^2) - Pi/4.
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EXAMPLE
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arctan(cos(x)^2) - Pi/4 = 0 - x^2/2 - 2*x^4/4! + 44*x^6/6! + 1408*x^8/8! + ...
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MATHEMATICA
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Part[#, Range[1, Length[#], 2]] &@(Array[#! &, Length[#], 0]*#) &@
CoefficientList[Series[ArcTan[Cos[x]^2] - Pi/4, {x, 0, 30}], x] // ExpandAll
With[{nn=30}, Take[CoefficientList[Series[ArcTan[Cos[x]^2]-Pi/4, {x, 0, nn}], x] Range[0, nn]!, {1, -1, 2}]] (* Harvey P. Dale, Feb 24 2022 *)
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CROSSREFS
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KEYWORD
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sign
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AUTHOR
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STATUS
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approved
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