%I #22 Oct 25 2014 11:17:28
%S 1,1,2,1,2,3,1,2,6,4,1,2,12,24,5,1,2,24,576,120,6,1,2,48,55296,161280,
%T 720,7,1,2,96,36972288,2781803520,812851200,5040,8,1,2,192,
%U 6268637952000,52260618977280,994393803303936000,61479419904000,40320,9
%N Array read by antidiagonals upwards: T(d,n) = number of d-dimensional permutations of n letters (d >= 0, n >= 1).
%C By definition, this is the number of nXnXnX...Xn = n^(d+1) arrays of 0's and 1's with exactly one 1 in each row, column, ..., line, ... .
%C An ordinary permutation is the case d = 1 (ordinary matrices with a single 1 in each row and column).
%C Rows d=2,3,... correspond to Latin squares, cubes, etc.
%H Linial, Nathan, and Zur Luria, <a href="http://arxiv.org/abs/1106.0649">An upper bound on the number of high-dimensional permutations</a>, arXiv preprint arXiv:1106.0649 [math.CO], (2011).
%H Linial, Nathan, and Zur Luria, <a href="http://dx.doi.org/10.1007/s00493-014-2842-8">An upper bound on the number of high-dimensional permutations</a>, Combinatorica, 34 (2014), 471-486.
%e The array begins:
%e d\n: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11,
%e --------------------------------------------------------------
%e 0: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11,
%e 1: 1, 2, 6, 24, 120, 720, 5040, 40320, 362880, 3628800, 39916800, ...
%e 2: 1, 2, 12, 576, 161280, 812851200, 61479419904000, 108776032459082956800,...
%e 3: 1, 2, 24, 55296, 2781803520, 994393803303936000, ...
%e 4: 1, 2, 48, 36972288, 52260618977280, ...
%e 5: 1, 2, 96, 6268637952000, 2010196727432478720, ...
%e 6: 1, 2, 192, ...
%e 7: 1, 2, 384, ...
%e 8: 1, 2, 768, ...
%e ...
%Y Rows: A000142, A002860, A098679, A100540, A132206.
%Y Column 4 = A249028.
%Y See A249027 for another version.
%K nonn,tabl
%O 0,3
%A _N. J. A. Sloane_, Oct 23 2014