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Search: id:A079268
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| A079268 |
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d(n,k) = number of decreasing labeled trees with n nodes and largest leaf <= k. |
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+0
2
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| 1, 1, 1, 1, 3, 3, 1, 7, 15, 15, 1, 15, 57, 105, 105, 1, 31, 195, 561, 945, 945, 1, 63, 633, 2685, 6555, 10395, 10395, 1, 127, 1995, 12105, 40725, 89055, 135135, 135135, 1, 255, 6177, 52605, 237555, 684495, 1381905, 2027025, 2027025, 1, 511, 18915, 223161
(list; table; graph; listen)
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OFFSET
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1,5
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REFERENCES
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J. L. Martin, The slopes determined by n points in the plane, preprint, 2003.
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LINKS
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J. L. Martin, The slopes determined by n points in the plane.
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FORMULA
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Recurrence: d(n, k) = 1 for n=0 or k=1, d(n, k) = 0 for n>0 and either k<0 or k>n, d(n, k) = d(n-1, k) + d(n, k-1) + sum( binomial(k-1, w)*binomial(n-k, x)*d(n-k+w-x, w+1)*d(k-w+x, k-w-1), w=0..k-2, x=0..n-k-1)
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EXAMPLE
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Table begins
1
1 1
1 3 3
1 7 15 15
1 15 57 105 105
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CROSSREFS
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First two columns are A000012 and A000225, rightmost two diagonals are both A001147, difference of second- and third-rightmost diagonals is A000165.
Sequence in context: A114422 A127501 A118408 this_sequence A102316 A133709 A124040
Adjacent sequences: A079265 A079266 A079267 this_sequence A079269 A079270 A079271
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KEYWORD
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easy,nonn,tabl
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AUTHOR
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Jeremy Martin (martin(AT)math.umn.edu), Feb 05 2003
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