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Search: id:A127121
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| A127121 |
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Number of endofunctions on a set, where the multiset of indegrees forms the n-th partition in Mathematica order (ignoring 0's). |
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+0
2
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| 1, 1, 1, 2, 1, 3, 3, 1, 3, 3, 7, 5, 1, 3, 4, 8, 10, 14, 7, 1, 3, 4, 8, 3, 19, 17, 6, 32, 26, 11, 1, 3, 4, 8, 4, 19, 18, 11, 14, 63, 34, 29, 75, 45, 15, 1, 3, 4, 8, 4, 19, 18, 3, 20, 14, 64, 37, 14, 39, 85, 168, 62, 15, 109, 167, 75, 22, 1, 3, 4, 8, 4, 19, 18, 4, 20, 14, 64, 38, 11, 26, 71
(list; graph; listen)
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OFFSET
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0,4
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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). In the first, node 1 has indegree 3, the next 3 node 1 has indegree 2 and node 2 has indegree 1 (forming partition [2,1]) and the final 3 are permutations, each node having indegree 1. The partitions of 3 in Mathematica order are [3], [2,1], [1^3], so row 3 of the triangle is 1,3,3.
The triangle starts:
1
1
1 2
1 3 3
1 3 3 7 5
1 3 4 8 10 14 7
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CROSSREFS
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Sequence in context: A126572 A162910 A098975 this_sequence A049834 A134625 A054531
Adjacent sequences: A127118 A127119 A127120 this_sequence A127122 A127123 A127124
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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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