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A113946
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Series expansion of Farey rational polynomial based on A112627.
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0
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1, 5, 23, 81, 367, 1297, 5871, 20753, 93935, 332049, 1502959, 5312785, 24047343, 85004561, 384757487, 1360072977, 6156119791, 21761167633, 98497916655, 348178682129, 1575966666479, 5570858914065, 25215466663663, 89133742625041
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OFFSET
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0,2
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COMMENTS
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Polynomial expanded is constant*(x+1/2)^2*(1+2x)/(1-x-16x^2+16x^3) the Jasinski rational polynomial p[x_] = (9/32)*(x + 1/2)^3/((x - 1/4)*(x + 1/4)*(x + 1)) f[x_] := 1/p[x] /; 0 <= x <= 1/2 f[x_] := p[x] /; 1/2 < x <= 1 gives a Farey like function with maximum at 1.
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LINKS
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FORMULA
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b(n) = coefficient series expansion of (9/32)*(x + 1/2)^3/((x - 1/4)*(x + 1/4)*(x + 1)) a(n) = (-16/9)*b(n).
a(n) = (5*(-4)^n+4*(-1)^n+81*4^n)/60 for n>0. G.f.: -(2*x+1)^3 / ((x+1)*(4*x-1)*(4*x+1)). [Colin Barker, Dec 03 2012]
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MATHEMATICA
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b = -(16/9)*ReplacePart[Table[Coefficient[Series[(9/32)*(x + 1/2)^3/((x - 1/4)*(x + 1/4)*(x + 1)), {x, 0, 30}], x^n], {n, 0, 30}], -9/16, 1]
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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