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Search: id:A122176
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| A122176 |
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Triangle, read by rows, where T(n,k) = C( k*(k+1)/2 + n-k + 1, n-k) for n>=k>=0. |
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+0
6
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| 1, 2, 1, 3, 3, 1, 4, 6, 5, 1, 5, 10, 15, 8, 1, 6, 15, 35, 36, 12, 1, 7, 21, 70, 120, 78, 17, 1, 8, 28, 126, 330, 364, 153, 23, 1, 9, 36, 210, 792, 1365, 969, 276, 30, 1, 10, 45, 330, 1716, 4368, 4845, 2300, 465, 38, 1, 11, 55, 495, 3432, 12376, 20349, 14950, 4960, 741, 47, 1
(list; table; graph; listen)
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OFFSET
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0,2
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COMMENT
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Remarkably, column k of the matrix inverse (A121436) equals signed column k of matrix power: A107876^(k*(k+1)/2 + 2).
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EXAMPLE
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Triangle begins:
1;
2, 1;
3, 3, 1;
4, 6, 5, 1;
5, 10, 15, 8, 1;
6, 15, 35, 36, 12, 1;
7, 21, 70, 120, 78, 17, 1;
8, 28, 126, 330, 364, 153, 23, 1;
9, 36, 210, 792, 1365, 969, 276, 30, 1; ...
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PROGRAM
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(PARI) T(n, k)=if(n<k|k<0, 0, binomial(k*(k+1)/2+n-k+1, n-k))
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CROSSREFS
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Cf. A121436 (inverse); variants: A098568, A122175, A122177.
Sequence in context: A130305 A144400 A143328 this_sequence A159881 A098546 A126277
Adjacent sequences: A122173 A122174 A122175 this_sequence A122177 A122178 A122179
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KEYWORD
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nonn,tabl
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AUTHOR
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Paul D. Hanna (pauldhanna(AT)juno.com), Aug 25 2006
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