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 A249026 Array read by antidiagonals upwards: T(d,n) = number of d-dimensional permutations of n letters (d >= 0, n >= 1). 7
 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, 720, 7, 1, 2, 96, 36972288, 2781803520, 812851200, 5040, 8, 1, 2, 192, 6268637952000, 52260618977280, 994393803303936000, 61479419904000, 40320, 9 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS 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, ... . An ordinary permutation is the case d = 1 (ordinary matrices with a single 1 in each row and column). Rows d=2,3,... correspond to Latin squares, cubes, etc. LINKS Linial, Nathan, and Zur Luria, An upper bound on the number of high-dimensional permutations, arXiv preprint arXiv:1106.0649 [math.CO], (2011). Linial, Nathan, and Zur Luria, An upper bound on the number of high-dimensional permutations, Combinatorica, 34 (2014), 471-486. EXAMPLE The array begins: d\n: 1, 2, 3,  4,  5,   6,   7,    8,     9,      10,      11, -------------------------------------------------------------- 0:   1, 2, 3,  4,  5,   6,   7,    8,     9,      10,      11, 1:   1, 2, 6,  24, 120, 720, 5040, 40320, 362880, 3628800, 39916800,  ... 2:   1, 2, 12, 576, 161280, 812851200, 61479419904000, 108776032459082956800,... 3:   1, 2, 24, 55296, 2781803520, 994393803303936000, ... 4:   1, 2, 48, 36972288, 52260618977280, ... 5:   1, 2, 96, 6268637952000, 2010196727432478720, ... 6:   1, 2, 192, ... 7:   1, 2, 384, ... 8:   1, 2, 768, ... ... CROSSREFS Rows: A000142, A002860, A098679, A100540, A132206. Column 4 = A249028. See A249027 for another version. Sequence in context: A263736 A126247 A213999 * A263597 A263905 A263693 Adjacent sequences:  A249023 A249024 A249025 * A249027 A249028 A249029 KEYWORD nonn,tabl AUTHOR N. J. A. Sloane, Oct 23 2014 STATUS approved

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Last modified October 22 12:45 EDT 2018. Contains 316458 sequences. (Running on oeis4.)