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Search: id:A056860
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| A056860 |
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Triangle T(n,k) = number of element-subset partitions of {1..n} with n-k+1 equalities (n >= 1, 1<=k<=n). |
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3
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| 1, 1, 1, 1, 2, 2, 1, 3, 6, 5, 1, 4, 12, 20, 15, 1, 5, 20, 50, 75, 52, 1, 6, 30, 100, 225, 312, 203, 1, 7, 42, 175, 525, 1092, 1421, 877, 1, 8, 56, 280, 1050, 2912, 5684, 7016, 4140, 1, 9, 72, 420, 1890, 6552, 17052, 31572, 37260, 21147
(list; table; graph; listen)
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OFFSET
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1,5
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COMMENT
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T(n,k) = number of permutations on [n] with n in position k in which 321 patterns only occur as part of 3241 patterns. Example: T(4,2)=3 counts 1423, 2413, 3412. - David Callan (callan(AT)stat.wisc.edu), Jul 20 2005
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REFERENCES
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W. C. Yang, Conjectures on some sequences involving set partitions and Bell numbers, preprint, 2000.
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LINKS
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David Callan, A combinatorial interpretation of the eigensequence for composition
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FORMULA
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T(n, k)=binom(n-1, k-1)B(k-1) where B denotes the Bell numbers A000110. - David Callan (callan(AT)stat.wisc.edu), Jul 20 2005
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CROSSREFS
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Essentially same as A056857, where rows are read from left to right.
Adjacent sequences: A056857 A056858 A056859 this_sequence A056861 A056862 A056863
Sequence in context: A091187 A065173 A098474 this_sequence A107111 A082037 A110858
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KEYWORD
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nonn,tabl,easy
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AUTHOR
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njas, Oct 13 2000
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EXTENSIONS
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More terms from David Callan (callan(AT)stat.wisc.edu), Jul 20 2005
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