A370771 - OEIS

%I #8 Mar 02 2024 03:16:21

%S 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,

%T 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,

%U 7434,4784,895,135,25,6,2,1,1,1,1842,35381,32372,6846,915,135,25,6,2,1,1

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

%C A front is a k-clique.

%H Andrew Gainer-Dewar, <a href="https://doi.org/10.37236/2615">Gamma-Species and the Enumeration of k-Trees</a>, Electronic Journal of Combinatorics, Volume 19 (2012), #P45.

%e Triangle begins:

%e   1;

%e   1,   1;

%e   1,   1,    1;

%e   1,   2,    1,    1;

%e   1,   4,    2,    1,   1;

%e   1,   9,    6,    2,   1,   1;

%e   1,  20,   21,    6,   2,   1,  1;

%e   1,  48,   83,   25,   6,   2,  1, 1;

%e   1, 115,  356,  126,  25,   6,  2, 1, 1;

%e   1, 286, 1599,  745, 135,  25,  6, 2, 1, 1;

%e   1, 719, 7434, 4784, 895, 135, 25, 6, 2, 1, 1;

%e   ...

%Y Columns k=0..2 are A000012, A000081, A058866.

%Y Cf. A370770 (unrooted), A370772, A370773.

%K nonn,tabl

%O 0,8

%A _Andrew Howroyd_, Mar 01 2024