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A157327
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Egyptian fraction expansion for Pi/4 = arctan(1/2) + arctan(1/3) (Hutton 1776).
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2
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2, 3, -24, -81, 160, 1215, -896, -15309, 4608, 177147, -22528, -1948617, 106496, 20726199, -491520, -215233605, 2228224, 2195382771, -9961472, -22082967873, 44040192, 219667417263, -192937984, -2165293113021, 838860800
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OFFSET
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0,1
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COMMENTS
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Sum_{n>=0} 1/a(n) = Pi/4.
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LINKS
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FORMULA
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G.f.: 2*(1-4*x^2)/(1+4*x^2)^2 + 3*x*(1-9*x^2)/(1+9*x^2)^2.
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MATHEMATICA
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CoefficientList[Series[2 (1 - 4 x^2)/(1 + 4 x^2)^2 + 3 x (1 - 9 x^2)/(1 + 9 x^2)^2, {x, 0, 40}], x] (* Vincenzo Librandi, Dec 12 2012 *)
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CROSSREFS
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KEYWORD
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frac,sign
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AUTHOR
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STATUS
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approved
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