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Search: id:A056859
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| A056859 |
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Triangle of number of falls in set partitions of n. |
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1
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| 1, 2, 0, 4, 1, 0, 8, 7, 0, 0, 16, 32, 4, 0, 0, 32, 121, 49, 1, 0, 0, 64, 411, 360, 42, 0, 0, 0, 128, 1304, 2062, 624, 22, 0, 0, 0, 256, 3949, 10163, 6042, 730, 7, 0, 0, 0, 512, 11567, 45298, 45810, 12170, 617, 1, 0, 0, 0, 1024, 33056, 187941, 296017, 141822, 18325
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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Number of falls s_i > s_{i+1} 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.
The maximum number of falls is in a set partition like 1,2,1,3,2,1,... - Frank Adams-Watters (FrankTAW(AT)Netscape.net), Jun 08 2006
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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 1 fall, at i = 2.
1; 2,0; 4,1,0; 8,7,0,0; 16,32,4,0,0; 32,121,49,1,0,0; ...
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CROSSREFS
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Cf. Bell numbers A000110.
Cf. A056857-A056863.
Sequence in context: A022904 A019215 A112081 this_sequence A090888 A020781 A007432
Adjacent sequences: A056856 A056857 A056858 this_sequence A056860 A056861 A056862
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KEYWORD
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easy,nonn,tabf
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AUTHOR
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Winston C. Yang (winston(AT)cs.wisc.edu), Aug 31 2000
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EXTENSIONS
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Corrected and extended by Frank Adams-Watters (FrankTAW(AT)Netscape.net), Jun 08 2006
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