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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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

REFERENCES

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

LINKS

Table of n, a(n) for n=1..24.

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.

Simon Plouffe, 1031 Generating Functions and Conjectures, Université du Québec à Montréal, 1992.

Index entries for sequences related to trees

FORMULA

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

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 by Simon Plouffe in his 1992 dissertation.

CROSSREFS

Sequence in context: A296190 A263552 A259839 * A034668 A215854 A123358

Adjacent sequences:  A005171 A005172 A005173 * A005175 A005176 A005177

KEYWORD

nonn

AUTHOR

N. J. A. Sloane.

STATUS

approved

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Last modified December 6 04:14 EST 2019. Contains 329784 sequences. (Running on oeis4.)