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Search: id:A134829
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| A134829 |
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Denominator of moments of Chebyshev U- (or S-) polynomials. |
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+0
2
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| 1, 1, 4, 1, 8, 1, 64, 1, 128, 1, 512, 1, 1024, 1, 16384, 1, 32768, 1, 131072, 1, 262144, 1, 2097152, 1, 4194304, 1, 16777216, 1, 33554432, 1, 1073741824, 1, 2147483648, 1, 8589934592, 1, 17179869184, 1, 137438953472, 1, 274877906944, 1, 1099511627776
(list; graph; listen)
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OFFSET
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0,3
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COMMENT
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The numerators are given in A134828.
The weight function for Chebyshev's U-polynomials is w(x)=sqrt(1-x^2)*2/Pi for x in [ -1,+1]. For the S-polynomials S(n,x)=U(n,x/2) on [ -2,+2] it is sqrt(1-x^2)/Pi. For the coefficient of the S-polynomials see A049310.
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LINKS
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W. Lang, Rationals and more.
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FORMULA
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a(n)= denominator(r(n)) with r(n):=int((2/Pi)*sqrt(1-x^2)*x^n,x=-1..+1), n>=0.
a(n)=1 if n is odd, a(n)=denominator(C(n/2)/2^n) if n is even, with the Catalan numbers C(n):=A000108(n).
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EXAMPLE
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Rationals: [1, 0, 1/4, 0, 1/8, 0, 5/64, 0, 7/128, 0, 21/512, 0, 33/1024, 0,...].
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CROSSREFS
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Cf. A120777 (coincides with denominators for even n).
Adjacent sequences: A134826 A134827 A134828 this_sequence A134830 A134831 A134832
Sequence in context: A019425 A080102 A106475 this_sequence A130297 A112032 A145917
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KEYWORD
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nonn,easy,frac
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AUTHOR
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Wolfdieter Lang (wolfdieter.lang(AT)physik.uni-karlsruhe.de) Jan 21 2008
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