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A370772
Triangle read by rows: T(n,k) is the number of k-trees with n unlabeled nodes rooted at a hedron.
3
0, 1, 0, 1, 1, 0, 1, 1, 1, 0, 1, 3, 1, 1, 0, 1, 6, 3, 1, 1, 0, 1, 16, 10, 3, 1, 1, 0, 1, 37, 39, 10, 3, 1, 1, 0, 1, 96, 164, 48, 10, 3, 1, 1, 0, 1, 239, 746, 253, 48, 10, 3, 1, 1, 0, 1, 622, 3474, 1584, 273, 48, 10, 3, 1, 1, 0, 1, 1607, 16658, 10500, 1913, 273, 48, 10, 3, 1, 1, 0
OFFSET
0,12
COMMENTS
A hedron is a (k+1)-clique.
LINKS
Andrew Gainer-Dewar, Gamma-Species and the Enumeration of k-Trees, Electronic Journal of Combinatorics, Volume 19 (2012), #P45.
EXAMPLE
Triangle begins:
0;
1, 0;
1, 1, 0;
1, 1, 1, 0;
1, 3, 1, 1, 0;
1, 6, 3, 1, 1, 0;
1, 16, 10, 3, 1, 1, 0;
1, 37, 39, 10, 3, 1, 1, 0;
1, 96, 164, 48, 10, 3, 1, 1, 0;
1, 239, 746, 253, 48, 10, 3, 1, 1, 0;
1, 622, 3474, 1584, 273, 48, 10, 3, 1, 1, 0;
...
CROSSREFS
Columns k=1..2 are A027852, A063688(n-2).
Cf. A370770 (unrooted), A370771, A370773.
Sequence in context: A244657 A072024 A238010 * A011354 A143119 A220419
KEYWORD
nonn,tabl
AUTHOR
Andrew Howroyd, Mar 01 2024
STATUS
approved