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A005174
Number of trees of subsets of an n-set.
(Formerly M4738)
1
0, 0, 10, 124, 890, 5060, 25410, 118524, 527530, 2276020, 9613010, 40001324, 164698170, 672961380, 2734531810, 11066546524, 44652164810, 179768037140, 722553165810, 2900661482124, 11634003919450, 46630112719300, 186802788139010, 748058256616124
OFFSET
1,3
REFERENCES
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
LINKS
F. R. McMorris and T. Zaslavsky,The number of cladistic characters,Math. Biosciences, 54 (1981), 3-10.
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; arXiv:0911.4975 [math.NT], 2009.
Simon Plouffe,1031 Generating Functions,Appendix to Thesis, Montreal, 1992.
FORMULA
The 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
Formula of Layman matches the proven formula in McMorris and Zaslavsky. -Sean A. Irvine,Apr 12 2016
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
MAPLE
A005174:=2*z**2*(5+12*z)/(z-1)/(3*z-1)/(2*z-1)/(4*z-1); # conjectured bySimon Plouffein his 1992 dissertation
KEYWORD
nonn
STATUS
approved