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A370770 Triangle read by rows: T(n,k) is the number of k-trees with n unlabeled nodes.

%I A370770 #8 Mar 02 2024 03:15:04
%S A370770 1,1,1,1,1,1,1,1,1,1,1,2,1,1,1,1,3,2,1,1,1,1,6,5,2,1,1,1,1,11,12,5,2,
%T A370770 1,1,1,1,23,39,15,5,2,1,1,1,1,47,136,58,15,5,2,1,1,1,1,106,529,275,64,
%U A370770 15,5,2,1,1,1,1,235,2171,1505,331,64,15,5,2,1,1,1
%N A370770 Triangle read by rows: T(n,k) is the number of k-trees with n unlabeled nodes.
%H A370770 Allan Bickle, <a href="https://doi.org/10.20429/tag.2024.000105">A Survey of Maximal k-degenerate Graphs and k-Trees</a>, Theory and Applications of Graphs 0 1 (2024) Article 5.
%H A370770 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.
%H A370770 I. M. Gessel and A. Gainer-Dewar, <a href="http://arxiv.org/abs/1309.1429">Counting unlabeled k-trees</a>, arXiv:1309.1429 [math.CO], 2013-2014.
%H A370770 I. M. Gessel and A. Gainer-Dewar, <a href="https://doi.org/10.1016/j.jcta.2014.05.002">Counting unlabeled k-trees</a>, J. Combin. Theory Ser. A 126 (2014), 177-193.
%H A370770 Andrew Howroyd, <a href="/A370770/a370770.txt">SageMath Program code</a> (from Andrew Gainer-Dewar reference).
%F A370770 T(n,k) = A370771(n,k) + A370772(n,k) - A370773(n,k).
%e A370770 Triangle begins:
%e A370770   1;
%e A370770   1,   1;
%e A370770   1,   1,   1;
%e A370770   1,   1,   1,   1;
%e A370770   1,   2,   1,   1,  1;
%e A370770   1,   3,   2,   1,  1,  1;
%e A370770   1,   6,   5,   2,  1,  1, 1;
%e A370770   1,  11,  12,   5,  2,  1, 1, 1;
%e A370770   1,  23,  39,  15,  5,  2, 1, 1, 1;
%e A370770   1,  47, 136,  58, 15,  5, 2, 1, 1, 1;
%e A370770   1, 106, 529, 275, 64, 15, 5, 2, 1, 1, 1;
%e A370770   ...
%Y A370770 Columns k=0..7 are A000012, A000055, A054581, A078792, A078793, A201702, A202037, A322754.
%Y A370770 Cf. A135021 (labeled version), A370771, A370772, A370773.
%K A370770 nonn,tabl
%O A370770 0,12
%A A370770 _Andrew Howroyd_, Mar 01 2024