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Search: id:A081277
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| A081277 |
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Square array of unsigned coefficients of Chebyshev polynomials of the first kind. |
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+0
5
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| 1, 1, 1, 1, 3, 2, 1, 5, 8, 4, 1, 7, 18, 20, 8, 1, 9, 32, 56, 48, 16, 1, 11, 50, 120, 160, 112, 32, 1, 13, 72, 220, 400, 432, 256, 64, 1, 15, 98, 364, 840, 1232, 1120, 576, 128, 1, 17, 128, 560, 1568, 2912, 3584, 2816, 1280, 256, 1, 19, 162, 816, 2688, 6048, 9408, 9984, 6912
(list; table; graph; listen)
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OFFSET
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0,5
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COMMENT
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Rows include A011782, A001792, A001793, A001794, A006974.
Formatted as a triangular array, this is [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, ...] DELTA [1, 1, 0, 0, 0, 0, 0, 0, 0, 0, ...] (see construction in A084938 ) . - Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Aug 09 2005
Antidiagonal sums are in A025192 . - Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Dec 04 2006
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FORMULA
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T(n, k) := (n+2k)C(n+k-1, k-1)2^(n-1)/k, k>0. T(n, 0) defined by G.f. (1-x)/(1-2x). Other rows are defined by (1-x)/(1-2x)^n.
T(n, 0) = 0 if n<0, T(0, k) = 0 if k<0, T(0, 0) = T(1, 0) = 1, T(n, k) = T(n, k-1) + 2*T(n-1, k); for example, 160 = 48 + 2*56 for n = 4 and k = 2 . -Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Aug 12 2005
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EXAMPLE
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Rows begin
1, 1, 2, 4, 8,...
1, 3, 8, 20, 48,...
1, 5, 18, 56, 160,...
1, 7, 32, 120, 400,...
1, 9, 50, 220, 840,...
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CROSSREFS
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Cf. A079628.
Sequence in context: A092879 A073370 A129675 this_sequence A079628 A140287 A077951
Adjacent sequences: A081274 A081275 A081276 this_sequence A081278 A081279 A081280
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KEYWORD
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easy,nonn,tabl
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AUTHOR
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Paul Barry (pbarry(AT)wit.ie), Mar 16 2003
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