

A005174


Number of trees of subsets of an nset.
(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
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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), 310.
F. R. McMorris and T. Zaslavsky, The number of cladistic characters, Math. Biosciences, 54 (1981), 310. [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)/(z1)/(3*z1)/(2*z1)/(4*z1); # 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



