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A298426
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Regular triangle where T(n,k) is number of k-ary rooted trees with n nodes.
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18
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1, 0, 1, 0, 1, 1, 0, 1, 0, 1, 0, 1, 1, 0, 1, 0, 1, 0, 0, 0, 1, 0, 1, 2, 1, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 1, 3, 0, 1, 0, 0, 0, 1, 0, 1, 0, 2, 0, 0, 0, 0, 0, 1, 0, 1, 6, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 11, 4, 2, 0, 1, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 23, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1
(list;
table;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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1,24
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COMMENTS
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LINKS
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EXAMPLE
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Triangle begins:
1
0 1
0 1 1
0 1 0 1
0 1 1 0 1
0 1 0 0 0 1
0 1 2 1 0 0 1
0 1 0 0 0 0 0 1
0 1 3 0 1 0 0 0 1
0 1 0 2 0 0 0 0 0 1
0 1 6 0 0 1 0 0 0 0 1
0 1 0 0 0 0 0 0 0 0 0 1
0 1 11 4 2 0 1 0 0 0 0 0 1
0 1 0 0 0 0 0 0 0 0 0 0 0 1
0 1 23 0 0 0 0 1 0 0 0 0 0 0 1
0 1 0 8 0 2 0 0 0 0 0 0 0 0 0 1
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MATHEMATICA
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nn=16;
arut[n_, k_]:=If[n===1, {{}}, Join@@Function[c, Union[Sort/@Tuples[arut[#, k]&/@c]]]/@Select[IntegerPartitions[n-1], Length[#]===k&]]
Table[arut[n, k]//Length, {n, nn}, {k, 0, n-1}]
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CROSSREFS
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Cf. A000005, A000081, A000598, A001190, A001678, A003238, A004111, A067538, A143773, A289078, A289079, A295461, A298118, A298422, A298423, A298424.
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KEYWORD
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AUTHOR
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STATUS
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approved
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