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Search: id:A056863
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| A056863 |
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Related to triangle of number of rises in set partitions of n at a given index i. |
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+0
7
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| 1, -1, 1, -2, 1, 1, -3, 4, 2, 1, -4, 9, 10, 4, 1, -5, 16, 28, 24, 8, 1, -6, 25, 60, 80, 56, 16
(list; table; graph; listen)
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OFFSET
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1,4
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COMMENT
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Number of rises in a set partition {s_1, ..., s_n} of {1, ..., n}, where s_i is the subset containing i, s(1) = 1 and s(i) <= 1 + max of previous s(j)'s.
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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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EXAMPLE
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For example {1, 2, 1, 2, 2, 3} is a set partition of {1, 2, 3, 4, 5, 6} and has 3 rises, at i = 1, i = 3 and i = 5.
1,-1; 1,-2,1; 1,-3,4,2; 1,-4,9,10,4; ...
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CROSSREFS
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Cf. Bell numbers A000110.
Cf. A056857-A056862.
Sequence in context: A093541 A089940 A123974 this_sequence A120019 A159933 A128314
Adjacent sequences: A056860 A056861 A056862 this_sequence A056864 A056865 A056866
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KEYWORD
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easy,sign,tabl,more
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AUTHOR
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Winston C. Yang (winston(AT)cs.wisc.edu), Aug 31 2000
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