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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. 1
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 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,14

REFERENCES

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

LINKS

Alois P. Heinz, Rows n = 0..100, flattened

FORMULA

G.f.: Sum(Product(1-1/(1+((1+x)^i-1)*y), i=1..n), n=0..infinity).

EXAMPLE

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.

Sequence in context: A098172 A049759 A265421 * A228623 A036875 A036877

Adjacent sequences:  A137249 A137250 A137251 * A137253 A137254 A137255

KEYWORD

nonn,tabl

AUTHOR

Vladeta Jovovic, Mar 11 2008

STATUS

approved

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Last modified September 27 15:44 EDT 2021. Contains 347691 sequences. (Running on oeis4.)