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A358575
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Triangle read by rows where T(n,k) is the number of unlabeled n-node rooted trees with k = 0..n-1 internal (non-leaf) nodes.
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15
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1, 0, 1, 0, 1, 1, 0, 1, 2, 1, 0, 1, 3, 4, 1, 0, 1, 4, 8, 6, 1, 0, 1, 5, 14, 18, 9, 1, 0, 1, 6, 21, 39, 35, 12, 1, 0, 1, 7, 30, 72, 97, 62, 16, 1, 0, 1, 8, 40, 120, 214, 212, 103, 20, 1, 0, 1, 9, 52, 185, 416, 563, 429, 161, 25, 1
(list;
table;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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1,9
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LINKS
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EXAMPLE
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Triangle begins:
1
0 1
0 1 1
0 1 2 1
0 1 3 4 1
0 1 4 8 6 1
0 1 5 14 18 9 1
0 1 6 21 39 35 12 1
0 1 7 30 72 97 62 16 1
0 1 8 40 120 214 212 103 20 1
0 1 9 52 185 416 563 429 161 25 1
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MATHEMATICA
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art[n_]:=If[n==1, {{}}, Join@@Table[Select[Tuples[art/@c], OrderedQ], {c, Join@@Permutations/@IntegerPartitions[n-1]}]];
Table[Length[Select[art[n], Count[#, _[__], {0, Infinity}]==k&]], {n, 1, 10}, {k, 0, n-1}]
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CROSSREFS
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Column k = n - 2 appears to be A002620.
Column k = 3 appears to be A006578.
The version for height instead of internal nodes is A034781.
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KEYWORD
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AUTHOR
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STATUS
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approved
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