A370771 Triangle read by rows: T(n,k) is the number of k-trees with n unlabeled nodes rooted at a front.

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

Table of n, a(n) for n=0..77.

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

Adjacent sequences: A370768 A370769 A370770 * A370772 A370773 A370774

Keyword

nonn,tabl

Author

Andrew Howroyd, Mar 01 2024

Status

approved