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A005173
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Number of trees of subsets of an n-set.
(Formerly M4844)
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2
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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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listen;
history;
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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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FORMULA
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G.f.: x*(1 + 6*x) / ((1 - x)*(1 - 2*x)*(1 - 3*x)). [corrected by Ray Chandler, Jun 26 2023]
First differences give A003063, 3^(n-1) - 2^n.
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MAPLE
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MATHEMATICA
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CoefficientList[Series[x (1+6 x)/(1-x)/(1-2 x)/(1-3 x), {x, 0, 30}], x] (* Harvey P. Dale, Jul 03 2023 *)
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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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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