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Search: id:A122175
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| A122175 |
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Triangle, read by rows, where T(n,k) = C( k*(k+1)/2 + n-k, n-k) for n>=k>=0. |
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6
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| 1, 1, 1, 1, 2, 1, 1, 3, 4, 1, 1, 4, 10, 7, 1, 1, 5, 20, 28, 11, 1, 1, 6, 35, 84, 66, 16, 1, 1, 7, 56, 210, 286, 136, 22, 1, 1, 8, 84, 462, 1001, 816, 253, 29, 1, 1, 9, 120, 924, 3003, 3876, 2024, 435, 37, 1, 1, 10, 165, 1716, 8008, 15504, 12650, 4495, 703, 46, 1, 1, 11, 220
(list; table; graph; listen)
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OFFSET
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0,5
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COMMENT
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Remarkably, column k of the matrix inverse (A121435) equals signed column k of matrix power: A107876^(k*(k+1)/2 + 1).
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EXAMPLE
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Triangle begins:
1;
1, 1;
1, 2, 1;
1, 3, 4, 1;
1, 4, 10, 7, 1;
1, 5, 20, 28, 11, 1;
1, 6, 35, 84, 66, 16, 1;
1, 7, 56, 210, 286, 136, 22, 1;
1, 8, 84, 462, 1001, 816, 253, 29, 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, n-k))
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CROSSREFS
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Cf. A121435 (inverse); variants: A098568, A122176, A122177.
Sequence in context: A009999 A098446 A098447 this_sequence A073165 A137153 A063841
Adjacent sequences: A122172 A122173 A122174 this_sequence A122176 A122177 A122178
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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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