A299907 Number of decomposable lonesum n X n (0,1) matrices.

1, 2, 16, 344, 13528, 833432, 73871416, 8893109864, 1394602938808, 275985896665592, 67227147723919096, 19756312865302785224, 6889612105281125091448, 2811911251972519547757272, 1327454489179890318710048056, 717555570945004782603934710824

Offset: 0

Author

N. J. A. Sloane, Feb 23 2018

Keywords

• nonn

Links

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

Crossrefs

Main diagonal of A299906.

See also A000629, A221961 for symmetric square lonesum matrices.

See A099594 for lonesum (0,1) matrices.

Programs

Mathematica

a[n_] := Sum[Binomial[j - 1 , k - 1 ]*j!^2*StirlingS2[n + 1, j + 1]^2/k!, {k, 0, n}, {j, k, n}]; Table[a[n], {n, 0, 15}] (* Jean-François Alcover, Feb 24 2018 *)

Extensions

More terms from Jean-François Alcover, Feb 24 2018