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Search: id:A100257
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| A100257 |
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Triangle of expansions of 2^(k-1)*x^k in terms of T(n,x), in descending degrees n of T, with T the Chebyshev polynomials. |
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17
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| 1, 1, 0, 1, 0, 1, 1, 0, 3, 0, 1, 0, 4, 0, 3, 1, 0, 5, 0, 10, 0, 1, 0, 6, 0, 15, 0, 10, 1, 0, 7, 0, 21, 0, 35, 0, 1, 0, 8, 0, 28, 0, 56, 0, 35, 1, 0, 9, 0, 36, 0, 84, 0, 126, 0, 1, 0, 10, 0, 45, 0, 120, 0, 210, 0, 126, 1, 0, 11, 0, 55, 0, 165, 0, 330, 0, 462, 0, 1, 0, 12, 0, 66, 0, 220, 0
(list; table; graph; listen)
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OFFSET
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0,9
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REFERENCES
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M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards Applied Math. Series 55, 1964 (and various reprintings), p. 795.
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LINKS
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M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards, Applied Math. Series 55, Tenth Printing, December 1972 [alternative scanned copy].
Index entries for sequences related to Chebyshev polynomials.
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EXAMPLE
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x^0 = T(0,x)
x^1 = T(1,x) + 0T(0,x)
2x^2 = T(2,x) + 0T(1,x) + 1T(0,x)
4x^3 = T(3,x) + 0T(2,x) + 3T(1,x) + 0T(0,x)
8x^4 = T(4,x) + 0T(3,x) + 4T(2,x) + 0T(1,x) + 3T(0,x)
16x^5 = T(5,x) + 0T(4,x) + 5T(3,x) + 0T(2,x) + 10T(1,x) + 0T(0,x)
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PROGRAM
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(PARI) a(k, n)=if(k==1, 1, if(n%2==0||k<0||n>k, 0, if(n>=k-1, binomial(2*floor(k/2), floor(k/2))/2, binomial(k-1, floor(n/2)))))
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CROSSREFS
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Without zeros: A008311. Row sums are A011782. Cf. A092392.
Diagonals are (with interleaved zeros) twice A001700, A001791, A002054, A002694, A003516, A002696, A030053, A004310, A030054, A004311, A030055, A004312, A030056, A004313.
Adjacent sequences: A100254 A100255 A100256 this_sequence A100258 A100259 A100260
Sequence in context: A117178 A111527 A035695 this_sequence A100573 A049087 A046665
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KEYWORD
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nonn,tabl
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AUTHOR
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Ralf Stephan, Nov 13 2004
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