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.
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, 42, 171, 57, 1, 0, 0, 0, 0, 26, 507, 718, 120, 1, 0, 0, 0, 0, 8, 840, 4017, 2682, 247, 1, 0, 0, 0, 0, 1, 865, 12866, 25531, 9327, 502, 1, 0, 0, 0, 0, 0, 584, 26831, 138080, 141904, 30973, 1013, 1
Offset: 0
Examples
Triangle T(n,k) begins: 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, 42, 171, 57, 1; 0, 0, 0, 0, 26, 507, 718, 120, 1; ...
Links
- Alois P. Heinz, Rows n = 0..100, flattened
- Matthieu Dien, Antoine Genitrini, and Frederic Peschanski, A Combinatorial Study of Async/Await Processes, Conf.: 19th Int'l Colloq. Theor. Aspects of Comp. (2022), (Analytic) Combinatorics of concurrent systems.
- M. Dukes, S. Kitaev, J. Remmel, E. Steingrimsson, Enumerating (2+2)-free posets by indistinguishable elements, J. Combin. 2 (1) (2011) 139-163 doi:10.4310/JOC.2011.v2.n1.a6, Figure 2; arXiv preprint arXiv:1006.2696 [math.CO], 2010-2011.
Formula
G.f.: Sum(Product(1-1/(1+((1+x)^i-1)*y), i=1..n), n=0..infinity).