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A178693
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Numerators of coefficients of Maclaurin series for 2 - sqrt(1 - x - x^2).
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4
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1, 1, 5, 5, 45, 95, 465, 1165, 24445, 65595, 359915, 1003315, 11342185, 32415435, 187063145, 544172445, 25508284445, 75196195795, 445774614215, 1327748661015, 15887874844835, 47715177777185, 287618252461095, 869652752181595
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OFFSET
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0,3
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COMMENTS
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Every term after the second is a multiple of 5.
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REFERENCES
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M. Kauers and P. Paule, The Concrete Tetrahedron, Springer 2011, p. 41.
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LINKS
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FORMULA
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G.f.: 2 - sqrt(1 - x - x^2) for the fractions (not the numerators).
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EXAMPLE
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The Maclaurin series begins with 1 + (1/2)*x + (5/8)*x^2 + (5/16)*x^3 + ....
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MATHEMATICA
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Numerator[CoefficientList[Series[2-Sqrt[1-x-x^2], {x, 0, 30}], x]] (* G. C. Greubel, Jan 25 2019 *)
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PROG
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(PARI) my(x='x+O('x^30)); v=Vec( 2-sqrt(1-x-x^2) ); vector(#v, n, numerator(v[n])) \\ G. C. Greubel, Jan 25 2019
(Magma) m:=30; R<x>:=PowerSeriesRing(Rationals(), m); b:=Coefficients(R!( 2-Sqrt(1-x-x^2) )); [Numerator(Factorial(n-1)*b[n]): n in [1..m]]; // G. C. Greubel, Jan 25 2019
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CROSSREFS
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KEYWORD
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nonn,frac
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AUTHOR
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STATUS
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approved
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