This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A330490 #24 Dec 17 2019 02:39:50
%S A330490 1,1,1,1,2,1,1,6,5,1,1,24,70,15,1,1,120,2167,1574,52,1,1,720,130708,
%T A330490 968162,69874,203,1,1,5040,14231289
%N A330490 Total number of permutation arrays of side length n and dimension k as defined by Eriksson and Linusson (2000a); square array T(n,k), read by ascending antidiagonals, for n, k >= 1.
%C A330490 The poset P_{3 x 3} of (3 x 3 x 3)-permutation arrays is shown in Figure 1 on p. 209 of Eriksson and Linuson (2000a). We have |P_{3 x 3}| = T(3,3) = 70. The numbers in this rectangular array are copied from Table 1 (p. 210) of the same paper.
%H A330490 Kimmo Eriksson and Svante Linusson, <a href="https://doi.org/10.1006/aama.1999.0693">A combinatorial theory of higher-dimensional permutation arrays</a>, Adv. Appl. Math. 25(2) (2000a), 194-211.
%H A330490 Kimmo Eriksson and Svante Linusson, <a href="https://doi.org/10.1006/aama.2000.0694">A decomposition of Fl(n)^d indexed by permutation arrays</a>, Adv. Appl. Math. 25(2) (2000b), 212-227. [Fl(n)^d denotes the flag manifold over C^n.]
%F A330490 T(n=1,k) = 1 = A000012(n) and T(n=2,k) = A000110(k) (Bell numbers).
%F A330490 T(n,k=1) = 1 = A000012(n) and T(n,k=2) = n! = A000142(n).
%F A330490 T(n,k) >= (n!)^(k-1) = A225816(k-1, n).
%F A330490 T(n,k=3) <= n!*2^(binomial(n+1,2) - 1).
%e A330490 Array T(n,k) (with rows n >= 1 and columns k >= 1) begins as follows, where * indicates a missing number:
%e A330490 1, 1, 1, 1, 1, ...
%e A330490 1, 2, 5, 15, 52, ...
%e A330490 1, 6, 70, 1574, 69874, ...
%e A330490 1, 24, 2167, 968162, *, ...
%e A330490 1, 120, 130708, *, *, ...
%e A330490 1, 720, 14231289, *, *, ...
%e A330490 1, 5040, 2664334184, *, *, ...
%e A330490 1, 40320, 831478035698, *, *, ...
%e A330490 ...
%Y A330490 Cf. A000012, A000110, A000142, A225816.
%K A330490 nonn,tabl,more
%O A330490 1,5
%A A330490 _Petros Hadjicostas_, Dec 16 2019