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A005174 Number of trees of subsets of an n-set.
(Formerly M4738)
1

%I M4738

%S 0,0,10,124,890,5060,25410,118524,527530,2276020,9613010,40001324,

%T 164698170,672961380,2734531810,11066546524,44652164810,179768037140,

%U 722553165810,2900661482124,11634003919450,46630112719300,186802788139010,748058256616124

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

%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="http://dx.doi.org/10.1016/0025-5564(81)90071-7">The number of cladistic characters</a>, Math. Biosciences, 54 (1981), 3-10.

%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="http://www.lacim.uqam.ca/%7Eplouffe/articles/MasterThesis.pdf">Approximations de séries génératrices et quelques conjectures</a>, Dissertation, Université du Québec à Montréal, 1992.

%H Simon Plouffe, <a href="http://www.lacim.uqam.ca/%7Eplouffe/articles/FonctionsGeneratrices.pdf">1031 Generating Functions and Conjectures</a>, Université du Québec à Montréal, 1992.

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

%F The listed terms a(1) - a(18) are given by a(n)=(8/3)(4^n - 4) - 9(3^n) + 11(2^n) + 5 - _John W. Layman_, Jul 20 1999

%F Formula of Layman matches the proven formula in McMorris and Zaslavsky. - _Sean A. Irvine_, Apr 12 2016

%F E.g.f.: (1/3)*(-17*exp(x) + 66*exp(2*x) - 81*exp(3*x) + 32*exp(4*x)). - _Ilya Gutkovskiy_, Apr 12 2016

%p A005174:=2*z**2*(5+12*z)/(z-1)/(3*z-1)/(2*z-1)/(4*z-1); # Conjectured by _Simon Plouffe_ in his 1992 dissertation.

%K nonn

%O 1,3

%A _N. J. A. Sloane_.

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Last modified January 27 08:31 EST 2020. Contains 331293 sequences. (Running on oeis4.)