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A072574
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Triangle T(n,k) of number of compositions (unordered partitions) of n into exactly k distinct parts, 1<=k<=n.
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3
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1, 1, 0, 1, 2, 0, 1, 2, 0, 0, 1, 4, 0, 0, 0, 1, 4, 6, 0, 0, 0, 1, 6, 6, 0, 0, 0, 0, 1, 6, 12, 0, 0, 0, 0, 0, 1, 8, 18, 0, 0, 0, 0, 0, 0, 1, 8, 24, 24, 0, 0, 0, 0, 0, 0, 1, 10, 30, 24, 0, 0, 0, 0, 0, 0, 0, 1, 10, 42, 48, 0, 0, 0, 0, 0, 0, 0, 0, 1, 12, 48, 72, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 12, 60, 120, 0
(list; table; graph; refs; listen; history; internal format)
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OFFSET
| 1,5
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COMMENTS
| If terms in the compositions did not need to be distinct then the triangle would have values C(n-1,k-1), essentially A007318 offset.
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LINKS
| Index entries for sequences related to compositions
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FORMULA
| T(n, k) =T(n-k, k)+k*T(n-k, k-1) [with T(n, 0)=1 if n=0 and 0 otherwise] =A000142(k)*A060016(n, k).
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EXAMPLE
| T(6,2)=4 since 6 can be written as 1+5=2+4=4+2=5+1.
Triangle starts
1;
1, 0;
1, 2, 0;
1, 2, 0, 0;
1, 4, 0, 0, 0;
1, 4, 6, 0, 0, 0;
1, 6, 6, 0, 0, 0, 0;
1, 6, 12, 0, 0, 0, 0, 0;
1, 8, 18, 0, 0, 0, 0, 0, 0;
1, 8, 24, 24, 0, 0, 0, 0, 0, 0;
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CROSSREFS
| Columns (offset) include A057427 and A052928. Row sums are A032020. Cf. A060016, A072575, A072576.
Sequence in context: A101661 A079644 A072705 * A058650 A112177 A115723
Adjacent sequences: A072571 A072572 A072573 * A072575 A072576 A072577
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KEYWORD
| nonn,tabl
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AUTHOR
| Henry Bottomley (se16(AT)btinternet.com), Jun 21 2002
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