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A121334
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Triangle, read by rows, where T(n,k) = C( n*(n+1)/2 + n-k, n-k), for n>=k>=0.
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5
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1, 2, 1, 10, 4, 1, 84, 28, 7, 1, 1001, 286, 66, 11, 1, 15504, 3876, 816, 136, 16, 1, 296010, 65780, 12650, 2024, 253, 22, 1, 6724520, 1344904, 237336, 35960, 4495, 435, 29, 1, 177232627, 32224114, 5245786, 749398, 91390, 9139, 703, 37, 1, 5317936260
(list; table; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| A triangle having similar properties and complementary construction is the dual triangle A122175.
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FORMULA
| Remarkably, row n of the matrix inverse (A121439) equals row n of A121412^(-n*(n+1)/2-1). Further, the following matrix products of triangles of binomial coefficients are equal: A121412 = A121334*A122178^-1 = A121335*A121334^-1 = A121336*A121335^-1, where row n of H=A121412 equals row (n-1) of H^(n+1) with an appended '1'.
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EXAMPLE
| Triangle begins:
1;
2, 1;
10, 4, 1;
84, 28, 7, 1;
1001, 286, 66, 11, 1;
15504, 3876, 816, 136, 16, 1;
296010, 65780, 12650, 2024, 253, 22, 1;
6724520, 1344904, 237336, 35960, 4495, 435, 29, 1;
177232627, 32224114, 5245786, 749398, 91390, 9139, 703, 37, 1; ...
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PROG
| (PARI) T(n, k)=binomial(n*(n+1)/2+n-k, n-k)
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CROSSREFS
| Cf. A121439 (matrix inverse); A121412; variants: A122178, A121335, A121336; A122175 (dual).
Sequence in context: A110327 A105615 A136216 * A126450 A112333 A066868
Adjacent sequences: A121331 A121332 A121333 * A121335 A121336 A121337
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KEYWORD
| nonn,tabl
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AUTHOR
| Paul D. Hanna (pauldhanna(AT)juno.com), Aug 29 2006
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