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Search: id:A122177
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| A122177 |
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Triangle, read by rows, where T(n,k) = C( k*(k+1)/2 + n-k + 2, n-k) for n>=k>=0. |
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+0
6
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| 1, 3, 1, 6, 4, 1, 10, 10, 6, 1, 15, 20, 21, 9, 1, 21, 35, 56, 45, 13, 1, 28, 56, 126, 165, 91, 18, 1, 36, 84, 252, 495, 455, 171, 24, 1, 45, 120, 462, 1287, 1820, 1140, 300, 31, 1, 55, 165, 792, 3003, 6188, 5985, 2600, 496, 39, 1, 66, 220, 1287, 6435, 18564, 26334
(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 (A121437) equals signed column k of matrix power: A107876^(k*(k+1)/2 + 3) for k>=0.
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EXAMPLE
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Triangle begins:
1;
3, 1;
6, 4, 1;
10, 10, 6, 1;
15, 20, 21, 9, 1;
21, 35, 56, 45, 13, 1;
28, 56, 126, 165, 91, 18, 1;
36, 84, 252, 495, 455, 171, 24, 1;
45, 120, 462, 1287, 1820, 1140, 300, 31, 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+2, n-k))
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CROSSREFS
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Cf. A121437 (inverse); variants: A098568, A122175, A122176.
Sequence in context: A133110 A086270 A104712 this_sequence A108286 A131415 A121437
Adjacent sequences: A122174 A122175 A122176 this_sequence A122178 A122179 A122180
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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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