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Search: id:A129137
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| A129137 |
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Number of trees on [n], rooted at 1, in which 2 is a descendant of 3. |
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+0
5
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| 0, 0, 1, 5, 37, 366, 4553, 68408, 1206405, 24447440, 560041201, 14315792256, 404057805989, 12482986261760, 419042630871225, 15189786100468736, 591374264243364037, 24612549706061862912, 1090556290466098198625
(list; graph; listen)
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OFFSET
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1,4
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LINKS
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Washington G. Bomfim, Table of n, a(n) for n = 1..50
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FORMULA
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The following formula counts these trees by the length r of the path from 1 to 3: Sum_{r=1..n-2}(n-3)!n^(n-2-r)/(n-2-r)!.
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EXAMPLE
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a(4)=5 counts {1->3->2, 1->4}, {1->3->2, 3->4}, {1->3->2->4}, {1->3->4->2}, {1->4->3->2}.
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CROSSREFS
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Cf. A057500 = binom(n-1, 2)a(n).
Sequence in context: A025168 A084358 A050351 this_sequence A055869 A112937 A092649
Adjacent sequences: A129134 A129135 A129136 this_sequence A129138 A129139 A129140
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KEYWORD
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nonn
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AUTHOR
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David Callan (callan(AT)stat.wisc.edu), Mar 30 2007
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