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A370773
Triangle read by rows: T(n,k) is the number of k-trees with n unlabeled nodes rooted at a hedron with a designated front.
3
0, 1, 0, 1, 1, 0, 1, 2, 1, 0, 1, 5, 2, 1, 0, 1, 12, 7, 2, 1, 0, 1, 30, 26, 7, 2, 1, 0, 1, 74, 110, 30, 7, 2, 1, 0, 1, 188, 481, 159, 30, 7, 2, 1, 0, 1, 478, 2209, 940, 168, 30, 7, 2, 1, 0, 1, 1235, 10379, 6093, 1104, 168, 30, 7, 2, 1, 0, 1, 3214, 49868, 41367, 8428, 1124, 168, 30, 7, 2, 1, 0
OFFSET
0,8
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, 2, 1, 0;
1, 5, 2, 1, 0;
1, 12, 7, 2, 1, 0;
1, 30, 26, 7, 2, 1, 0;
1, 74, 110, 30, 7, 2, 1, 0;
1, 188, 481, 159, 30, 7, 2, 1, 0;
1, 478, 2209, 940, 168, 30, 7, 2, 1, 0;
1, 1235, 10379, 6093, 1104, 168, 30, 7, 2, 1, 0;
...
CROSSREFS
Columns k=1 is A000106.
Cf. A370770 (unrooted), A370771, A370772.
Sequence in context: A066603 A263339 A244372 * A119331 A351641 A291883
KEYWORD
nonn,tabl
AUTHOR
Andrew Howroyd, Mar 01 2024
STATUS
approved