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Search: id:A101270
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| A101270 |
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Triangle read by rows: T(n,k) is the coefficient of z^k in the numerator of the polynomial part of z^n*exp(-n*s), where s=hypergeom([1,1,3/2],[2,5/2],1/z^2)/(6z^2); related to Chebyshev's quadrature. |
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1
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| 0, 1, -1, 0, 3, 0, -1, 0, 2, 1, 0, -30, 0, 45, 0, 7, 0, -60, 0, 72, -1, 0, 21, 0, -105, 0, 105, 0, -149, 0, 2142, 0, -7560, 0, 6480, -43, 0, -2220, 0, 20790, 0, -56700, 0, 42525, 0, 53, 0, -2280, 0, 15120, 0, -33600, 0, 22400, -43, 0, 561, 0, -9900, 0, 49896, 0, -93555, 0, 56133, 0, -33889, 0, 817674, 0, -9163440, 0
(list; graph; listen)
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OFFSET
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1,5
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REFERENCES
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H. E. Salzer, Tables for facilitating the use of Chebyshev's quadrature formula, Journal of Mathematics and Physics, 26 (1947),191-194.
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LINKS
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Eric Weisstein's World of Mathematics, Chebyshev Quadrature
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EXAMPLE
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T(4,0)=1,T(4,1)=0,T(4,2)=-30,T(4,3)=0,T(4,4)=45 because
z^4*exp(-4s)=z^4-2z^2/3+1/45-32/(2835z^2)+O(1/z^4) = (45z^4-30z^2+1)/45 - 32/(2835z^2)+O(1/z^4)
Triangle begins:
0,1;
-1,0,3;
0,-1,0,2;
1,0,-30,0,45;
0,7,0,-60,0,72;
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CROSSREFS
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T(n,n)=A002680(n).
Sequence in context: A046094 A055976 A093684 this_sequence A007524 A109718 A053385
Adjacent sequences: A101267 A101268 A101269 this_sequence A101271 A101272 A101273
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KEYWORD
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sign,tabf
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AUTHOR
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Emeric Deutsch (deutsch(AT)duke.poly.edu), Jan 24 2005
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