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Search: id:A101124
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| A101124 |
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Number triangle associated to Chebyshev polynomials of first kind. |
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+0
3
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| 1, 0, 1, -1, 1, 1, 0, 1, 2, 1, 1, 1, 7, 3, 1, 0, 1, 26, 17, 4, 1, -1, 1, 97, 99, 31, 5, 1, 0, 1, 362, 577, 244, 49, 6, 1, 1, 1, 1351, 3363, 1921, 485, 71, 7, 1, 0, 1, 5042, 19601, 15124, 4801, 846, 97, 8, 1, -1, 1, 18817, 114243, 119071, 47525, 10081, 1351, 127, 9, 1, 0, 1, 70226, 665857, 937444, 470449, 120126, 18817, 2024, 161
(list; table; graph; listen)
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OFFSET
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0,9
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LINKS
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Index entries for sequences related to Chebyshev polynomials.
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FORMULA
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Number triangle S(n, k)=T(n-k, k), k<n, S(n, n)=1, 0 otherwise, where T(n, k)=(n/2)sum{j=0..floor(n/2), C(n-j, j)(-1)^j*(2k)^(n-2j)}; Columns have g.f. x^k(1-kx)/(1-2kx+x^2). Also, square array if(n=0, 1, T(n, k)) read by anti-diagonals.
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EXAMPLE
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As a number triangle, rows begin {1}, {0,1}, {-1,1,1}, {0,1,2,1},...
As a square array, rows begin
1,1,1,1,1,...
0,1,2,3,4,...
-1,1,7,17,31,...
0,1,26,99,244,...
1,1,97,577,1921,..
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CROSSREFS
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Columns include A001075, A001541, A001091, A001079, A023038, A011943. Row sums are A101125. Diagonal sums are A101126.
Cf. A053120.
Adjacent sequences: A101121 A101122 A101123 this_sequence A101125 A101126 A101127
Sequence in context: A049270 A025269 A137296 this_sequence A011127 A157117 A061538
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KEYWORD
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easy,sign,tabl
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AUTHOR
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Paul Barry (pbarry(AT)wit.ie), Dec 02 2004
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