cp's OEIS Frontend

A137252 Triangle T(n,k) read by rows: number of k X k triangular (0,1)-matrices with exactly n entries equal to 1 and no zero rows or columns.

%I A137252 #25 Sep 15 2022 07:52:54
%S A137252 1,0,1,0,0,1,0,0,1,1,0,0,0,4,1,0,0,0,4,11,1,0,0,0,1,33,26,1,0,0,0,0,
%T A137252 42,171,57,1,0,0,0,0,26,507,718,120,1,0,0,0,0,8,840,4017,2682,247,1,0,
%U A137252 0,0,0,1,865,12866,25531,9327,502,1,0,0,0,0,0,584,26831,138080,141904,30973,1013,1
%N A137252 Triangle T(n,k) read by rows: number of k X k triangular (0,1)-matrices with exactly n entries equal to 1 and no zero rows or columns.
%H A137252 Alois P. Heinz, <a href="/A137252/b137252.txt">Rows n = 0..100, flattened</a>
%H A137252 Matthieu Dien, Antoine Genitrini, and Frederic Peschanski, <a href="https://www.researchgate.net/publication/363253998_A_Combinatorial_Study_of_AsyncAwait_Processes">A Combinatorial Study of Async/Await Processes</a>, Conf.: 19th Int'l Colloq. Theor. Aspects of Comp. (2022), (Analytic) Combinatorics of concurrent systems.
%H A137252 M. Dukes, S. Kitaev, J. Remmel, E. Steingrimsson, <a href="https://doi.org/10.4310/JOC.2011.v2.n1.a6">Enumerating (2+2)-free posets by indistinguishable elements</a>, J. Combin. 2 (1) (2011) 139-163 doi:10.4310/JOC.2011.v2.n1.a6, Figure 2; <a href="http://arxiv.org/abs/1006.2696">arXiv preprint</a> arXiv:1006.2696 [math.CO], 2010-2011.
%F A137252 G.f.: Sum(Product(1-1/(1+((1+x)^i-1)*y), i=1..n), n=0..infinity).
%e A137252 Triangle T(n,k) begins:
%e A137252   1;
%e A137252   0, 1;
%e A137252   0, 0, 1;
%e A137252   0, 0, 1, 1;
%e A137252   0, 0, 0, 4,  1;
%e A137252   0, 0, 0, 4, 11,   1;
%e A137252   0, 0, 0, 1, 33,  26,   1;
%e A137252   0, 0, 0, 0, 42, 171,  57,   1;
%e A137252   0, 0, 0, 0, 26, 507, 718, 120,  1;
%e A137252   ...
%Y A137252 Cf. A138265 (row sums), A005321 (column sums), A135589.
%Y A137252 T(2n,n) gives A357140.
%K A137252 nonn,tabl
%O A137252 0,14
%A A137252 _Vladeta Jovovic_, Mar 11 2008