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Search: id:A147989
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| A147989 |
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Coefficients of factor polynomials U(n,x) associated with reciprocation. |
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+0
6
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| 1, 1, -1, 1, 1, -3, -1, 1, 1, 1, -7, -4, 13, 4, -7, -1, 1, 1, 1, -15, -11, 83, 45, -220, -88, 303, 88, -220, -45, 83, 11, -15, -1, 1, 1, 1, -31, -26, 413, 293, -3141, -1896, 15261, 7866, -50187, -22122, 115410, 43488, -189036, -60753, 222621, 60753, -189036
(list; table; graph; listen)
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OFFSET
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1,6
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COMMENT
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The zeros of U(n,x) and U(n,-x) are the zeros of S(n,x) at A147985.
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REFERENCES
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Clark Kimberling, "Polynomials associated with reciprocation," preprint, 2008.
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FORMULA
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For n>=5, U(n)=U(n,x)=U(n-1,x)*U(n-1,-x)+x*(x^2-1)*U(3,x)*U(3,-x)*U(4,x)*U(4,-x)***U(n-2,x)*U(n-2,-x), where U(3)=x^2+x-1, U(4)=x^4+x^3-3*x^2-x+1.
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EXAMPLE
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U(3)=x^2+x-1
U(4)=x^4+x^3-3*x^2-x+1
U(5)=x^8+x^7-7*x^6-4*x^5+13*x^4+4*x^3-7*x^2-x+1
so that as an array A147989 begins with
1 1 -1
1 1 -3 -1 1
1 1 -7 -4 13 4 -7 -1 1
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CROSSREFS
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Cf. A147985, A147986, A147987, A147988, A147990, A147991, A147992, A147993.
Sequence in context: A010122 A058663 A124371 this_sequence A119329 A054724 A061494
Adjacent sequences: A147986 A147987 A147988 this_sequence A147990 A147991 A147992
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KEYWORD
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sign,tabl
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AUTHOR
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Clark Kimberling (ck6(AT)evansville.edu), Nov 25 2008
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