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Search: id:A113968
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| A113968 |
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Series expansion of Farey rational polynomial based on A112627. |
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+0
1
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| 0, 0, 1, 1, 15, 17, 239, 273, 3823, 4369, 61167, 69905, 978671, 1118481, 15658735, 17895697, 250539759, 286331153, 4008636143, 4581298449, 64138178287, 73300775185, 1026210852591, 1172812402961, 16419373641455, 18764998447377
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OFFSET
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0,5
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COMMENT
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Polynomial expanded is:constant*x)^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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FORMULA
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b(n)=coefficient series expansion of (9/8)*x^2*(x + 1/2)/((x - 1/4)*(x + 1/4)*(x + 1)) a(n) = (-1/9)*b(n)
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MATHEMATICA
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b = -(1/9)*ReplacePart[Table[Coefficient[Series[(9/8)*x^2*(x + 1/2)/((x - 1/4)*(x + 1/4)*(x + 1)), {x, 0, 30}], x^n], {n, 0, 30}], 0, 1] (* removes zeros*) c = Flatten[Table[If[b[[n]] > 0, b[[n]], {}], {n, 1, Length[b]}]]
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CROSSREFS
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Cf. A112627.
Sequence in context: A124334 A002155 A091017 this_sequence A093812 A124609 A102500
Adjacent sequences: A113965 A113966 A113967 this_sequence A113969 A113970 A113971
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KEYWORD
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nonn
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AUTHOR
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Roger L. Bagula (rlbagulatftn(AT)yahoo.com), Jan 31 2006
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