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A006678
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Number of planted binary phylogenetic trees with n labels.
(Formerly M4232)
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1
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0, 1, 1, 6, 39, 390, 4815, 73080, 1304415, 26847450, 625528575, 16279193700, 468022452975, 14731683916950, 503880434632575, 18609309606888000, 738057377647965375, 31286068076704691250, 1411602439003747365375, 67543694966494692445500, 3416288904242387117319375
(list;
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refs;
listen;
history;
text;
internal format)
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OFFSET
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0,4
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REFERENCES
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Foulds, L. R.; Robinson, R. W. Enumeration of binary phylogenetic trees. Combinatorial mathematics, VIII (Geelong, 1980), pp. 187-202, Lecture Notes in Math., 884, Springer, Berlin-New York, 1981. Math. Rev. 83a:05071.
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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FORMULA
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E.g.f.: -(-1+(1-2*x-2*x^2)^(1/2))/(1+x), Simon Plouffe in his Master's Thesis, Uqam 1992.
a(n) ~ sqrt(6-2*sqrt(3)) * (1+sqrt(3))^(n-1) * n^(n-1) / exp(n). - Vaclav Kotesovec, Oct 01 2013
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MATHEMATICA
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CoefficientList[Series[-(-1+(1-2*x-2*x^2)^(1/2))/(1+x), {x, 0, 20}], x]* Range[0, 20]! (* Vaclav Kotesovec, Oct 01 2013 *)
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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