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Irregular triangle read by rows: row n gives numbers of rooted trees with n nodes (n >= 1) and omega-valency k (k >= 1).
5

%I #14 Feb 17 2018 21:12:39

%S 1,1,2,3,1,7,1,1,13,5,1,1,31,9,6,1,1,66,29,11,7,1,1,159,62,42,13,8,1,

%T 1,365,181,92,55,15,9,1,1,900,422,294,127,70,17,10,1,1,2162,1166,720,

%U 435,165,86,19,11,1,1,5417,2885,2119,1110,608,208,104,21,12,1,1

%N Irregular triangle read by rows: row n gives numbers of rooted trees with n nodes (n >= 1) and omega-valency k (k >= 1).

%C See A003120 for definitions.

%H J.-C. Arditti, <a href="http://dx.doi.org/10.1016/0012-365X(73)90135-0">Dénombrement des arborescences dont le graphe de comparabilité est Hamiltonien</a>, Discrete Math., 5 (1973), 189-200.

%e Triangle begins:

%e 1

%e 1

%e 2

%e 3, 1

%e 7, 1, 1

%e 13, 5, 1, 1

%e 31, 9, 6, 1, 1

%e 66, 29, 11, 7, 1, 1

%e 159, 62, 42, 13, 8, 1, 1

%e 365, 181, 92, 55, 15, 9, 1, 1

%e 900, 422, 294, 127, 70, 17, 10, 1, 1

%e 2162, 1166, 720, 435, 165, 86, 19, 11, 1, 1

%e 5417, 2885, 2119, 1110, 608, 208, 104, 21, 12, 1, 1

%e ...

%Y Columns give A003120, A193487, A193488, A193489, A193490. Row sums give A000081.

%K nonn,tabf

%O 1,3

%A _N. J. A. Sloane_, Jul 27 2011