login
A370771
Triangle read by rows: T(n,k) is the number of k-trees with n unlabeled nodes rooted at a front.
3
1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 4, 2, 1, 1, 1, 9, 6, 2, 1, 1, 1, 20, 21, 6, 2, 1, 1, 1, 48, 83, 25, 6, 2, 1, 1, 1, 115, 356, 126, 25, 6, 2, 1, 1, 1, 286, 1599, 745, 135, 25, 6, 2, 1, 1, 1, 719, 7434, 4784, 895, 135, 25, 6, 2, 1, 1, 1, 1842, 35381, 32372, 6846, 915, 135, 25, 6, 2, 1, 1
OFFSET
0,8
COMMENTS
A front is a k-clique.
LINKS
Andrew Gainer-Dewar, Gamma-Species and the Enumeration of k-Trees, Electronic Journal of Combinatorics, Volume 19 (2012), #P45.
EXAMPLE
Triangle begins:
1;
1, 1;
1, 1, 1;
1, 2, 1, 1;
1, 4, 2, 1, 1;
1, 9, 6, 2, 1, 1;
1, 20, 21, 6, 2, 1, 1;
1, 48, 83, 25, 6, 2, 1, 1;
1, 115, 356, 126, 25, 6, 2, 1, 1;
1, 286, 1599, 745, 135, 25, 6, 2, 1, 1;
1, 719, 7434, 4784, 895, 135, 25, 6, 2, 1, 1;
...
CROSSREFS
Columns k=0..2 are A000012, A000081, A058866.
Cf. A370770 (unrooted), A370772, A370773.
Sequence in context: A252890 A173398 A362905 * A368106 A368104 A104404
KEYWORD
nonn,tabl
AUTHOR
Andrew Howroyd, Mar 01 2024
STATUS
approved