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A079126
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Triangle T(n,k) of numbers of partitions of n into distinct positive integers <= k, 0<=k<=n.
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5
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1, 0, 1, 0, 0, 1, 0, 0, 1, 2, 0, 0, 0, 1, 2, 0, 0, 0, 1, 2, 3, 0, 0, 0, 1, 2, 3, 4, 0, 0, 0, 0, 2, 3, 4, 5, 0, 0, 0, 0, 1, 3, 4, 5, 6, 0, 0, 0, 0, 1, 3, 5, 6, 7, 8, 0, 0, 0, 0, 1, 3, 5, 7, 8, 9, 10, 0, 0, 0, 0, 0, 2, 5, 7, 9, 10, 11, 12, 0, 0, 0, 0, 0, 2, 5, 8, 10, 12, 13, 14, 15, 0, 0, 0, 0, 0, 1, 4, 8, 11
(list; table; graph; refs; listen; history; internal format)
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OFFSET
| 0,10
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COMMENTS
| T(n,n) = A000009(n), right side of the triangle;
T(n,k)=0 for n>0 and k < A002024(n); T(prime(n),n) = A067953(n) for n>0.
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LINKS
| Eric Weisstein's World of Mathematics, Partition Function Q.
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FORMULA
| T(n, k)=b(0, n, k), where b(m, n, k)=1+sum(b(i, j, k): m<i<j<k and i+j=n).
T(n, k) = coefficient of x^n in Product_{i=1..k} (1+x^i). - Vladeta Jovovic (vladeta(AT)eunet.rs), Aug 07 2003
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CROSSREFS
| Cf. A000009, A079122, A035294, A079124, A079125.
Differs from A026840 in having extra zeros at the ends of the rows.
Sequence in context: A035699 A132406 A197881 * A186336 A025891 A120630
Adjacent sequences: A079123 A079124 A079125 * A079127 A079128 A079129
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KEYWORD
| nonn,tabl
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AUTHOR
| Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Dec 27 2002
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