

A003228


Endpoints in trees with n nodes.
(Formerly M0351)


5



1, 2, 2, 5, 9, 21, 43, 101, 226, 556, 1333, 3365, 8500, 22007, 57258, 151264, 401761, 1077063, 2902599, 7871250, 21440642, 58672589, 161155637, 444240627, 1228400744, 3406668865, 9472308269, 26402207803, 73755064178
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OFFSET

1,2


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..29.
R. W. Robinson and A. J. Schwenk, The distribution of trees in a large random tree, Discr. Math., 12 (1975), 359372.
Eric Weisstein's World of Mathematics, Tree Leaf.
Index entries for sequences related to trees


FORMULA

a(n) = Sum_{k=1..n} k*c(n, k), where c(n, k) = A055290(n, k) has g.f. (1x+x*y)*B(x, y)+(1/2)*(B(x^2, y^2)B(x, y)^2) and B(x, y) is g.f. for A055372.


CROSSREFS

Cf. A000055, A003227, A055290, A055372.
Sequence in context: A002990 A060405 A326493 * A184713 A110182 A309867
Adjacent sequences: A003225 A003226 A003227 * A003229 A003230 A003231


KEYWORD

nonn


AUTHOR

N. J. A. Sloane.


EXTENSIONS

Corrected and extended with formula by Christian G. Bower, May 25 2000


STATUS

approved



