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

0,14

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).

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

Adjacent sequences: A137249 A137250 A137251 * A137253 A137254 A137255

Keyword

nonn,tabl

Author

Vladeta Jovovic, Mar 11 2008

Status

approved