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Triangle read by rows: number of generic n-rook placements with k rooks below the main diagonal.
2

%I #13 Oct 15 2020 16:34:43

%S 1,4,7,26,68,75,236,940,1090,1105,2752,16645,20360,20790,20821,39208,

%T 360081,464111,477242,478376,478439,660032,9202170,12492277,12933423,

%U 12974826,12977688,12977815

%N Triangle read by rows: number of generic n-rook placements with k rooks below the main diagonal.

%H E. Banaian, S. Butler, C. Cox, J. Davis, J. Landgraf and S. Ponce, <a href="http://arxiv.org/abs/1508.03673">A generalization of Eulerian numbers via rook placements</a>, arXiv:1508.03673 [math.CO], 2015.

%H A. N. Bhavale, B. N. Waphare, <a href="https://ajc.maths.uq.edu.au/pdf/78/ajc_v78_p073.pdf">Basic retracts and counting of lattices</a>, Australasian J. of Combinatorics (2020) Vol. 78, No. 1, 73-99.

%e Triangle begins:

%e 1,

%e 4,7,

%e 26,68,75,

%e 236,940,1090,1105,

%e 2752,16645,20360,20790,20821,

%e 39208,360081,464111,477242,478376,478439,

%e 660032,9202170,12492277,12933423,12974826,12977688,12977815,

%e ...

%K nonn,tabl,more

%O 1,2

%A _N. J. A. Sloane_, Mar 16 2016