A299905 Array read by antidiagonals: T(n,k) = number of n X k lonesum decomposable (0,1) matrices of decomposition order 2.

0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 12, 12, 0, 0, 0, 0, 50, 108, 50, 0, 0, 0, 0, 180, 660, 660, 180, 0, 0, 0, 0, 602, 3420, 5714, 3420, 602, 0, 0, 0, 0, 1932, 16212, 40860, 40860, 16212, 1932, 0, 0, 0, 0, 6050, 72828, 262010, 391500, 262010, 72828, 6050, 0, 0

Offset: 0

Author

N. J. A. Sloane, Feb 23 2018

Keywords

• nonn
• tabl

Examples

			Array begins:
0,0,0,0,0,0,...,
0,0,0,0,0,0,...,
0,0,2,12,50,180,...,
0,0,12,108,660,3420,...,
0,0,50,660,5714,40860,...,
0,0,180,3420,40860,39150,...,
...
		

Links

• Ken Kamano, Lonesum decomposable matrices, arXiv:1701.07157 [math.CO], 2017. Also Discrete Math., 341 (2018), 341-349.

Crossrefs

Cf. A299904, A299906.

Programs

Mathematica

T[n_, k_] := Sum[(1/2)*(j - 1 )*j!^2*StirlingS2[k + 1, j + 1]*StirlingS2[n + 1, j + 1], {j, 2, Min[k, n]}]; Table[T[n - k, k], {n, 0, 10}, {k, 0, n}] // Flatten (* Jean-François Alcover, Feb 24 2018 *)

Extensions

More terms from Jean-François Alcover, Feb 24 2018