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Search: id:A005640
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| A005640 |
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Number of phylogenetic trees with n labels.
(Formerly M1896)
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+0
5
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| 1, 1, 2, 8, 64, 832, 15104, 352256, 10037248, 337936384, 13126565888, 577818263552, 28425821618176, 1545553369366528, 92034646352592896, 5956917762776367104, 416397789920380321792, 31262503202358260924416
(list; graph; listen)
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OFFSET
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0,3
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COMMENT
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Each node of the tree is a subset of the labeled set {1,...,n}. If the subset node is empty, it must have degree at least 3.
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REFERENCES
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N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
L. R. Foulds and R. W. Robinson, Determining the asymptotic number of phylogenetic trees, pp. 110-126 of Combinatorial Mathematics VII (Newcastle, August 1979), ed. R. W. Robinson, G. W. Southern and W. D. Wallis. Lect. Notes Math., 829. Springer, 1980.
J. P. Hayes, Enumeration of fanout-free Boolean functions, J. ACM, 23 (1976), 700-709.
K. L. Kodandapani and S. C. Seth, On combinational networks with restricted fan-out, IEEE Trans. Computers, 27 (1978), 309-318.
R. P. Stanley, Enumerative Combinatorics, Cambridge, Vol. 2, 1999; see Problem 5.26.
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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 A005263. E.g.f.: 1+B(x)-B(x)^2 where B(x) is e.g.f. of A005172.
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CROSSREFS
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For n >= 2, A005640(n) = 2^n*A006351(n) = 2^(n+1)*A000311(n).
Sequence in context: A136282 A092934 A139679 this_sequence A153540 A153568 A153531
Adjacent sequences: A005637 A005638 A005639 this_sequence A005641 A005642 A005643
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KEYWORD
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nonn,nice,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, formula and comment from Christian G. Bower (bowerc(AT)usa.net), Nov 15 1999.
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