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.

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

Author

Andrew Howroyd, Mar 01 2024

Keywords

• nonn
• tabl

Examples

			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;
  ...
		

Links

• Andrew Gainer-Dewar, Gamma-Species and the Enumeration of k-Trees, Electronic Journal of Combinatorics, Volume 19 (2012), #P45.

Crossrefs

Columns k=1 is A000106.

Cf. A370770 (unrooted), A370771, A370772.