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A005173 Number of trees of subsets of an n-set.
(Formerly M4844)
1

%I M4844

%S 0,1,12,61,240,841,2772,8821,27480,84481,257532,780781,2358720,

%T 7108921,21392292,64307941,193185960,580082161,1741295052,5225982301,

%U 15682141200,47054812201,141181213812,423577195861,1270798696440

%N Number of trees of subsets of an n-set.

%D F. R. McMorris and T. Zaslavsky, The number of cladistic characters, Math. Biosciences, 54 (1981), 3-10.

%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

%H F. R. McMorris and T. Zaslavsky, <a href="/A005172/a005172.pdf">The number of cladistic characters</a>, Math. Biosciences, 54 (1981), 3-10. [Annotated scanned copy]

%H Simon Plouffe, <a href="https://arxiv.org/abs/0911.4975">Approximations de séries génératrices et quelques conjectures</a>, Dissertation, Université du Québec à Montréal, 1992.

%H Simon Plouffe, <a href="/A000051/a000051_2.pdf">1031 Generating Functions</a>, Appendix to Thesis, Montreal, 1992

%H <a href="/index/Tra#trees">Index entries for sequences related to trees</a>

%F G.f.: x ( 1 + 6 x ) / ( 1 - x ) ( 1 - 2 x ) ( 1 - 3 x ).

%F First differences give A003063, 3^(n-1)-2^n.

%p A005173:=-z*(1+6*z)/(z-1)/(3*z-1)/(2*z-1); [Conjectured by _Simon Plouffe_ in his 1992 dissertation.]

%K nonn,easy

%O 1,3

%A _N. J. A. Sloane_.

%E More terms from Larry Reeves (larryr(AT)acm.org), Feb 06 2001

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Last modified May 7 10:32 EDT 2021. Contains 343650 sequences. (Running on oeis4.)