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Search: id:A122178
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| A122178 |
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Triangle, read by rows, where T(n,k) = C( n*(n+1)/2 + n-k - 1, n-k), for n>=k>=0. |
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+0
5
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| 1, 1, 1, 6, 3, 1, 56, 21, 6, 1, 715, 220, 55, 10, 1, 11628, 3060, 680, 120, 15, 1, 230230, 53130, 10626, 1771, 231, 21, 1, 5379616, 1107568, 201376, 31465, 4060, 406, 28, 1, 145008513, 26978328, 4496388, 658008, 82251, 8436, 666, 36, 1, 4431613550
(list; table; graph; listen)
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OFFSET
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0,4
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COMMENT
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A triangle having similar properties and complementary construction is the dual triangle A098568.
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FORMULA
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Remarkably, row n of the matrix inverse (A121438) equals row n of A121412^(-n*(n+1)/2). 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
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Triangle begins:
1;
1, 1;
6, 3, 1;
56, 21, 6, 1;
715, 220, 55, 10, 1;
11628, 3060, 680, 120, 15, 1;
230230, 53130, 10626, 1771, 231, 21, 1;
5379616, 1107568, 201376, 31465, 4060, 406, 28, 1;
145008513, 26978328, 4496388, 658008, 82251, 8436, 666, 36, 1; ...
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PROGRAM
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(PARI) T(n, k)=binomial(n*(n+1)/2+n-k-1, n-k)
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CROSSREFS
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Cf. A121438 (matrix inverse); A121412; variants: A121334, A121335, A121336; A098568 (dual).
Adjacent sequences: A122175 A122176 A122177 this_sequence A122179 A122180 A122181
Sequence in context: A066717 A119743 A108451 this_sequence A126445 A033326 A068996
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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 29 2006
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