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A299905 Array read by antidiagonals: T(n,k) = number of n X k lonesum decomposable (0,1) matrices of decomposition order 2. 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 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,13

LINKS

Table of n, a(n) for n=0..65.

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

EXAMPLE

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,...,

...

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 *)

CROSSREFS

Cf. A299904, A299906.

Sequence in context: A184366 A230614 A230730 * A225783 A135468 A003196

Adjacent sequences:  A299902 A299903 A299904 * A299906 A299907 A299908

KEYWORD

nonn,tabl

AUTHOR

N. J. A. Sloane, Feb 23 2018

EXTENSIONS

More terms from Jean-François Alcover, Feb 24 2018

STATUS

approved

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Last modified May 13 14:25 EDT 2021. Contains 343859 sequences. (Running on oeis4.)