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Search: id:A005805
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| A005805 |
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Number of phylogenetic trees with n labels.
(Formerly M1519)
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+0
3
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| 1, 2, 5, 18, 107, 1008, 13113, 214238, 4182487, 94747196, 2440784645, 70431957258, 2249856084803, 78802876705608, 3002702793753489, 123649410977736950, 5471808106109912815, 258948617502187143188
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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Series-reduced trees where each leaf is a non-empty subset of the set of n labels.
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REFERENCES
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Foulds, L. R.; Robinson, R. W. Enumeration of phylogenetic trees without points of degree two. Ars Combin. 17 (1984), A, 169-183. Math. Rev. 85f:05045
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
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N. J. A. Sloane, Transforms
Index entries for sequences related to trees
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FORMULA
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Stirling transform of [ 1, 1, 1, 4, 26, 236, ... ] = A000311(n-1).
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MAPLE
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stirtr:= proc(p) proc (n) add (p(k) *combinat[stirling2] (n, k), k=0..n) end end: b:= proc(n) option remember; if n<=1 then n elif n=2 then 1 else (n+1) *b(n-1) +2*add (binomial(n-1, k) *b(k) *b(n-k), k=2..n-2) fi end: a:= stirtr (n->`if` (n<2, 1, b(n-1))): seq (a(n), n=1..20); [From Alois P. Heinz (heinz(AT)hs-heilbronn.de), Sep 15 2008]
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CROSSREFS
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Cf. A000311, A005804.
Sequence in context: A005639 A093730 A007769 this_sequence A058338 A006896 A125625
Adjacent sequences: A005802 A005803 A005804 this_sequence A005806 A005807 A005808
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KEYWORD
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nonn,easy
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
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More terms, comment from Christian G. Bower (bowerc(AT)usa.net), Dec 15 1999.
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