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A005173
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Number of trees of subsets of an n-set.
(Formerly M4844)
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1
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0, 1, 12, 61, 240, 841, 2772, 8821, 27480, 84481, 257532, 780781, 2358720, 7108921, 21392292, 64307941, 193185960, 580082161, 1741295052, 5225982301, 15682141200, 47054812201, 141181213812, 423577195861, 1270798696440
(list;
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OFFSET
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1,3
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REFERENCES
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F. R. McMorris and T. Zaslavsky, The number of cladistic characters, Math. Biosciences, 54 (1981), 3-10.
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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Table of n, a(n) for n=1..25.
F. R. McMorris and T. Zaslavsky, The number of cladistic characters, Math. Biosciences, 54 (1981), 3-10. [Annotated scanned copy]
Simon Plouffe, Approximations de séries génératrices et quelques conjectures, Dissertation, Université du Québec à Montréal, 1992.
Simon Plouffe, 1031 Generating Functions, Appendix to Thesis, Montreal, 1992
Index entries for sequences related to trees
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FORMULA
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G.f.: x ( 1 + 6 x ) / ( 1 - x ) ( 1 - 2 x ) ( 1 - 3 x ).
First differences give A003063, 3^(n-1)-2^n.
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MAPLE
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A005173:=-z*(1+6*z)/(z-1)/(3*z-1)/(2*z-1); [Conjectured by Simon Plouffe in his 1992 dissertation.]
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CROSSREFS
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Sequence in context: A240002 A114241 A127766 * A196144 A294682 A177677
Adjacent sequences: A005170 A005171 A005172 * A005174 A005175 A005176
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KEYWORD
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nonn,easy
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AUTHOR
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N. J. A. Sloane.
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EXTENSIONS
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More terms from Larry Reeves (larryr(AT)acm.org), Feb 06 2001
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STATUS
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approved
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