OFFSET
1,3
COMMENTS
Number of unlabeled rooted trees with n nodes and a distinguished leaf. - Gus Wiseman, Jul 31 2018
REFERENCES
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
LINKS
R. W. Robinson and A. J. Schwenk, The distribution of trees in a large random tree, Discr. Math., 12 (1975), 359-372.
Eric Weisstein's World of Mathematics, Tree Leaf.
FORMULA
a(n) = Sum_{k=1..n} k*A055277(n, k).
EXAMPLE
The a(4) = 8 rooted trees with a distinguished leaf are (((O))), ((Oo)), ((oO)), (O(o)), (o(O)), (Ooo), (oOo), (ooO). - Gus Wiseman, Jul 31 2018
MATHEMATICA
urt[n_]:=Join@@Table[Union[Sort/@Tuples[urt/@ptn]], {ptn, IntegerPartitions[n-1]}];
Table[Sum[Length[Flatten[{t/.{}->1}]], {t, urt[n]}], {n, 15}] (* Gus Wiseman, Jul 31 2018 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
EXTENSIONS
Corrected and extended with formula by Christian G. Bower, May 25 2000
STATUS
approved