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A316772
Number of series-reduced locally nonintersecting rooted trees whose leaves form an integer partition of n.
0
1, 1, 2, 4, 11, 27, 75, 202, 565, 1602, 4617, 13472, 39781, 118604, 356605, 1080178, 3293109, 10097356, 31118507, 96341035
OFFSET
1,3
COMMENTS
A rooted tree is series-reduced if all non-leaf nodes have at least two branches. It is locally nonintersecting if the intersection of all branches directly under any given root is empty.
EXAMPLE
The a(6) = 27 trees:
6,
(15),
(24),
(1(14)), (114),
(1(23)), (2(13)), (3(12)), (123),
(1(1(13))), (1(113)), (11(13)), (1113),
(1(2(12))), (1(122)), (2(1(12))), (2(112)), (12(12)), (1122),
(1(1(1(12)))), (1(1(112))), (1(11(12))), (1(1112)), (11(1(12))), (11(112)), (111(12)), (11112).
MATHEMATICA
nms[n_]:=nms[n]=Prepend[Join@@Table[Select[Union[Sort/@Tuples[nms/@ptn]], Intersection@@#=={}&], {ptn, Rest[IntegerPartitions[n]]}], {n}];
Table[Length[nms[n]], {n, 10}]
KEYWORD
nonn,more
AUTHOR
Gus Wiseman, Jul 12 2018
EXTENSIONS
a(17)-a(20) from Robert Price, Sep 14 2018
STATUS
approved