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Search: id:A127124
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| A127124 |
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Number of endofunctions whose component sizes form the n-th partition in Mathematica order. |
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+0
2
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| 1, 1, 2, 1, 4, 2, 1, 9, 4, 3, 2, 1, 20, 9, 8, 4, 3, 2, 1, 51, 20, 18, 9, 10, 8, 4, 4, 3, 2, 1, 125, 51, 40, 20, 36, 18, 9, 10, 12, 8, 4, 4, 3, 2, 1, 329, 125, 102, 51, 80, 40, 20, 45, 36, 27, 18, 9, 20, 10, 12, 8, 4, 5, 4, 3, 2, 1, 862, 329, 250, 125, 204, 102, 51, 180, 80, 60, 40, 20, 45
(list; graph; listen)
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OFFSET
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0,3
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COMMENT
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Can be regarded as a triangle with one row for each size of partition.
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EXAMPLE
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For n = 3, the 7 endofunctions are (1,2,3) -> (1,1,1), (1,1,2), (1,2,1), (2,1,1), (1,2,3), (1,3,2) and (2,3,1). The components are respectively 123, 123, 13|2, 123, 1|2|3, 1|23 and 123, corresponding to partitions [3], [3], [2,1], [3], [1^3], [2,1] and [3]. The partitions of 3 in Mathematica order are [3], [2,1] and [1^3], so row 3 is 4,2,1.
The triangle starts:
1
1
2 1
4 2 1
9 4 3 2 1
20 9 8 4 3 2 1
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CROSSREFS
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Sequence in context: A123486 A158264 A158982 this_sequence A127136 A145983 A120025
Adjacent sequences: A127121 A127122 A127123 this_sequence A127125 A127126 A127127
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KEYWORD
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nonn,tabf
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AUTHOR
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Franklin T. Adams-Watters (FrankTAW(AT)Netscape.net), Jan 05 2007
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