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A339590 Irregular triangle read by rows: T(n,k) (n>=2, k>=1) = number of strong tournaments on n nodes with k descents.

%I A339590 #15 Jan 01 2021 15:30:47
%S A339590 0,1,1,1,6,10,6,1,1,13,56,123,158,123,56,13,1,1,22,172,717,1910,3547,
%T A339590 4791,4791,3547,1910,717,172,22,1,1,33,402,2674,11614,36293,86305,
%U A339590 161529,242890,297003,297003,242890,161529,86305,36293,11614,2674,402,33,1
%N A339590 Irregular triangle read by rows: T(n,k) (n>=2, k>=1) = number of strong tournaments on n nodes with k descents.
%D A339590 Archer, K., Gessel, I. M., Graves, C., & Liang, X. (2020). Counting acyclic and strong digraphs by descents. Discrete Mathematics, 343(11), 112041.
%H A339590 Kassie Archer, Ira M. Gessel, Christina Graves, and Xuming Liang, <a href="https://arxiv.org/abs/1909.01550">Counting acyclic and strong digraphs by descents</a>, arXiv:1909.01550 [math.CO], 20 Mar 2020.
%e A339590 Triangle begins:
%e A339590 0;
%e A339590 1, 1;
%e A339590 1, 6, 10, 6, 1;
%e A339590 1, 13, 56, 123, 158, 123, 56, 13, 1;
%e A339590 1, 22, 172, 717, 1910, 3547, 4791, 4791, 3547, 1910, 717, 172, 22, 1;
%e A339590 1, 33, 402, 2674, 11614, 36293, 86305, 161529, 242890, 297003, 297003, 242890, 161529, 86305, 36293, 11614, 2674, 402, 33, 1;
%e A339590 ...
%Y A339590 Row sums are A054946.
%Y A339590 Cf. A057273, A339807.
%K A339590 nonn,tabf
%O A339590 2,5
%A A339590 _N. J. A. Sloane_, Dec 28 2020