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A299904 Array read by antidiagonals: T(n,k) = number of n X k lonesum decomposable (0,1) matrices of decomposition order 1.

%I A299904 #13 Feb 24 2018 07:49:42
%S A299904 0,0,0,0,1,0,0,3,3,0,0,7,13,7,0,0,15,45,45,15,0,0,31,145,229,145,31,0,
%T A299904 0,63,453,1065,1065,453,63,0,0,127,1393,4717,6901,4717,1393,127,0,0,
%U A299904 255,4245,20265,41505,41505,20265,4245,255,0,0,511,12865,85309,237685,329461,237685,85309,12865,511,0
%N A299904 Array read by antidiagonals: T(n,k) = number of n X k lonesum decomposable (0,1) matrices of decomposition order 1.
%H A299904 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 A299904 Array begins:
%e A299904 0,0,0,0,0,0,...,
%e A299904 0,1,3,7,15,31,...,
%e A299904 0,3,13,45,145,453,...,
%e A299904 0,7,45,229,1065,4717,...,
%e A299904 0,15,145,1065,6901,41505,...,
%e A299904 0,31,453,4717,41505,32946,...,
%e A299904 ...
%t A299904 T[n_, k_] := Sum[j!^2*StirlingS2[k + 1, j + 1]*StirlingS2[n + 1, j + 1], {j, 1, Min[k, n]}]; Table[T[n - k, k], {n, 0, 10}, {k, 0, n}] // Flatten (* _Jean-François Alcover_, Feb 24 2018 *)
%Y A299904 Cf. A299905, A299906.
%K A299904 nonn,tabl
%O A299904 0,8
%A A299904 _N. J. A. Sloane_, Feb 23 2018
%E A299904 More terms from _Jean-François Alcover_, Feb 24 2018