%I #15 Oct 25 2019 18:09:50
%S 1,2,16,344,13528,833432,73871416,8893109864,1394602938808,
%T 275985896665592,67227147723919096,19756312865302785224,
%U 6889612105281125091448,2811911251972519547757272,1327454489179890318710048056,717555570945004782603934710824
%N Number of decomposable lonesum n X n (0,1) matrices.
%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.
%t 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 *)
%Y Main diagonal of A299906.
%Y See also A000629, A221961 for symmetric square lonesum matrices.
%Y See A099594 for lonesum (0,1) matrices.
%K nonn
%O 0,2
%A _N. J. A. Sloane_, Feb 23 2018
%E More terms from _Jean-François Alcover_, Feb 24 2018