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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.
4
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
0,14
LINKS
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).
EXAMPLE
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;
...
CROSSREFS
Cf. A138265 (row sums), A005321 (column sums), A135589.
T(2n,n) gives A357140.
Sequence in context: A049759 A355829 A265421 * A228623 A036875 A036877
KEYWORD
nonn,tabl
AUTHOR
Vladeta Jovovic, Mar 11 2008
STATUS
approved