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Search: id:A006964
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| A006964 |
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Number of directed rooted trees with n nodes.
(Formerly M2994)
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+0
4
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| 1, 3, 15, 82, 495, 3144, 20875, 142773, 1000131, 7136812, 51702231, 379234623, 2810874950, 21020047557, 158398829121, 1201617201230, 9169060501023, 70329406653879, 541949364313821, 4193569906262874
(list; graph; listen)
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OFFSET
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1,2
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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).
P. Leroux and B. Miloudi, ``G\'{e}n\'{e}ralisations de la formule d'Otter,'' Ann. Sci. Math. Qu\'{e}bec, Vol. 16, No. 1, pp. 53-80, 1992.
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LINKS
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INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 439
Index entries for sequences related to rooted trees
Index entries for sequences related to trees
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FORMULA
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a(n+1) has g.f.: prod from n =1 to inf ( 1 - x^3 a(n) )^-1.
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MAPLE
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with (numtheory): a:= proc(n) option remember; local d, j; if n<=1 then n else (add (d*a(d)*3, d=divisors(n-1)) +add (add (d*a(d), d=divisors(j)) *a(n-j)*3, j=1..n-2))/(n-1) fi end: seq (a(n), n=1..20); [From Alois P. Heinz (heinz(AT)hs-heilbronn.de), Sep 06 2008]
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CROSSREFS
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Cf. A038059.
Sequence in context: A084208 A059271 A014276 this_sequence A052451 A026019 A118356
Adjacent sequences: A006961 A006962 A006963 this_sequence A006965 A006966 A006967
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KEYWORD
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nonn,eigen
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AUTHOR
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Simon Plouffe (simon.plouffe(AT)gmail.com)
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EXTENSIONS
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Also rooted trees with n nodes and 3-colored non-root nodes.
Extended with alternative description by Christian G. Bower (bowerc(AT)usa.net), Apr 15 1998.
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