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Search: id:A134828
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| A134828 |
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Numerator of moments of Chebyshev U- (or S-) polynomials. |
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+0
2
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| 1, 0, 1, 0, 1, 0, 5, 0, 7, 0, 21, 0, 33, 0, 429, 0, 715, 0, 2431, 0, 4199, 0, 29393, 0, 52003, 0, 185725, 0, 334305, 0, 9694845, 0, 17678835, 0, 64822395, 0, 119409675, 0, 883631595, 0, 1641030105, 0, 6116566755, 0, 11435320455, 0, 171529806825, 0
(list; graph; listen)
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OFFSET
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0,7
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COMMENT
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The denominators are given in A134829.
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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)= numerator(r(n)) with r(n):=int((2/Pi)*sqrt(1-x^2)*x^n,x=-1..+1), n>=0.
a(n)=0 if n is odd, a(n)=numerator(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. A098597 (coincides with numerators for even n).
Sequence in context: A069206 A091685 A062824 this_sequence A070595 A021873 A020801
Adjacent sequences: A134825 A134826 A134827 this_sequence A134829 A134830 A134831
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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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