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A220905 Triangle read by rows: rook numbers of certain "probleme des rencontres" boards of the second kind of size n X k (0 <= k <= n).

%I A220905 #19 Dec 26 2015 14:20:24
%S A220905 1,1,0,1,2,0,1,6,6,2,1,24,132,176,24,1,60,960,4580,5040,552,1,120,
%T A220905 4260,52960,213000,206592,21280,1,210,14070,368830,3762360,13109712,
%U A220905 11404960,1073160
%N A220905 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 A220905 Rows 0 through 2 were not given in the reference and should be checked. (There is a Maple program in the Appendix).
%C A220905 What are the row sums?
%H A220905 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 A220905 Triangle begins:
%e A220905   1
%e A220905   1,   0
%e A220905   1,   2,     0
%e A220905   1,   6,     6,      2
%e A220905   1,  24,   132,    176,      24
%e A220905   1,  60,   960,   4580,    5040,      552
%e A220905   1, 120,  4260,  52960,  213000,   206592,    21280
%e A220905   1, 210, 14070, 368830, 3762360, 13109712, 11404960, 1073160
%e A220905   ...
%Y A220905 Right-hand diagonal is A000186.
%K A220905 nonn,tabl
%O A220905 0,5
%A A220905 _N. J. A. Sloane_, Jan 02 2013