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Triangle read by rows: rook numbers of certain "probleme des rencontres" boards of the second kind of size n X k (0 <= k <= n).
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%I #19 Dec 26 2015 14:20:24

%S 1,1,0,1,2,0,1,6,6,2,1,24,132,176,24,1,60,960,4580,5040,552,1,120,

%T 4260,52960,213000,206592,21280,1,210,14070,368830,3762360,13109712,

%U 11404960,1073160

%N Triangle read by rows: rook numbers of certain "probleme des rencontres" boards of the second kind of size n X k (0 <= k <= n).

%C Rows 0 through 2 were not given in the reference and should be checked. (There is a Maple program in the Appendix).

%C What are the row sums?

%H F. Alayont and N. Krzywonos, <a href="http://faculty.gvsu.edu/alayontf/notes/rook_polynomials_higher_dimensions_preprint.pdf">Rook Polynomials in Three and Higher Dimensions</a>, 2012.

%e Triangle begins:

%e 1

%e 1, 0

%e 1, 2, 0

%e 1, 6, 6, 2

%e 1, 24, 132, 176, 24

%e 1, 60, 960, 4580, 5040, 552

%e 1, 120, 4260, 52960, 213000, 206592, 21280

%e 1, 210, 14070, 368830, 3762360, 13109712, 11404960, 1073160

%e ...

%Y Right-hand diagonal is A000186.

%K nonn,tabl

%O 0,5

%A _N. J. A. Sloane_, Jan 02 2013