A352460 Triangle read by rows: T(n,k), 2 <= k < n is the number of n-element k-ary unlabeled rooted trees where a subtree consisting of h + 1 nodes has exactly min{h,k} subtrees.
1, 1, 1, 2, 1, 1, 2, 2, 1, 1, 4, 3, 2, 1, 1, 5, 4, 3, 2, 1, 1, 9, 6, 5, 3, 2, 1, 1, 13, 10, 6, 5, 3, 2, 1, 1, 23, 15, 10, 7, 5, 3, 2, 1, 1, 35, 24, 14, 10, 7, 5, 3, 2, 1, 1, 61, 39, 23, 14, 11, 7, 5, 3, 2, 1, 1, 98, 63, 34, 21, 14, 11, 7, 5, 3, 2, 1, 1
Offset: 3
Examples
Triangle begins:
1;
1, 1;
2, 1, 1;
2, 2, 1, 1;
4, 3, 2, 1, 1;
5, 4, 3, 2, 1, 1;
9, 6, 5, 3, 2, 1, 1;
13, 10, 6, 5, 3, 2, 1, 1;
23, 15, 10, 7, 5, 3, 2, 1, 1;
35, 24, 14, 10, 7, 5, 3, 2, 1, 1;
61, 39, 23, 14, 11, 7, 5, 3, 2, 1, 1;
98, 63, 34, 21, 14, 11, 7, 5, 3, 2, 1, 1;
In particular, the rooted trees counted in the first three rows of the triangle are shown by using the Hasse diagram as follows:
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o o
\ /
o
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o |
| |
o o | o o o
\ / | \ | /
o | o
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o o o o | o |
\ / | | | | |
o o o o | o o o | o o o o
\ / \ / | \ | / | \ \ / /
o o | o | o