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

%I #14 Feb 24 2018 07:49:05

%S 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,

%T 180,660,660,180,0,0,0,0,602,3420,5714,3420,602,0,0,0,0,1932,16212,

%U 40860,40860,16212,1932,0,0,0,0,6050,72828,262010,391500,262010,72828,6050,0,0

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

%H Ken Kamano, <a href="https://arxiv.org/abs/1701.07157">Lonesum decomposable matrices</a>, arXiv:1701.07157 [math.CO], 2017. Also Discrete Math., 341 (2018), 341-349.

%e Array begins:

%e 0,0,0,0,0,0,...,

%e 0,0,0,0,0,0,...,

%e 0,0,2,12,50,180,...,

%e 0,0,12,108,660,3420,...,

%e 0,0,50,660,5714,40860,...,

%e 0,0,180,3420,40860,39150,...,

%e ...

%t 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 *)

%Y Cf. A299904, A299906.

%K nonn,tabl

%O 0,13

%A _N. J. A. Sloane_, Feb 23 2018

%E More terms from _Jean-François Alcover_, Feb 24 2018