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 A287378 #29 Apr 29 2019 05:19:24
%S A287378 1,1,1,1,1,1,1,1,1,45360,1,1,10080,7484544,20432442240,1,1,226800,
%T A287378 2554075440,29331862801920,577185873264000000
%N A287378 Triangle read by rows: T(n,m) is the number of inequivalent n X m matrices under action of the Klein group, with one-eighth each of 1's, 2's, 3's, 4's, 5's, 6's, 7's and 8's (ordered occurrences rounded up/down if n*m != 0 mod 8).
%C A287378 Computed using Polya's enumeration theorem for coloring.
%H A287378 María Merino, <a href="/A287378/b287378.txt">Rows n=0..35 of triangle, flattened</a>
%H A287378 M. Merino and I. Unanue, <a href="https://doi.org/10.1387/ekaia.17851">Counting squared grid patterns with Pólya Theory</a>, EKAIA, 34 (2018), 289-316 (in Basque).
%F A287378 g(x1,x2,x3,x4,x5,x6,x7,x8) = (y1^(m*n) + 3*y2^(m*n/2))/4 for even n and m;
%F A287378 (y1^(m*n) + y1^n*y2^((m*n-m)/2) + 2*y2^(m*n/2))/4 for odd n and even m;
%F A287378 (y1^(m*n) + y1^m*y2^((m*n-n)/2) + 2*y2^(m*n/2))/4 for even n and odd m;
%F A287378 (y1^(m*n) + y1^n*y2^((m*n-n)/2) + y1^m*y2^((m*n-m)/2) + y1*y2^((m*n-1)/2))/4 for odd n and m, where the coefficients y1 and y2 correspond to y1 = Sum_{i=1..8} x_i and y2 = Sum_{i=1..8} x_i^2. Occurrences of numbers are ceiling(m*n/8) for the first k numbers and floor(m*n/8) for the last (8-k) numbers, if m*n = k mod 8.
%e A287378 For n = 4 and m = 2, the T(4,2) = 10080 solutions are colorings of 4 X 2 matrices in 8 colors inequivalent under the action of the Klein group with exactly 1 occurrence of each color (coefficient of x1^1, x2^1, x3^1, x4^1, x5^1, x6^1, x7^1, x8^1).
%e A287378 Triangle begins:
%e A287378 =================================================================
%e A287378 n\m | 0 1 2 3 4 5
%e A287378 ----|------------------------------------------------------------
%e A287378 0 | 1
%e A287378 1 | 1 1
%e A287378 2 | 1 1 1
%e A287378 3 | 1 1 1 45360
%e A287378 4 | 1 1 10080 7484544 20432442240
%e A287378 5 | 1 1 226800 2554075440 29331862801920 577185873264000000
%Y A287378 Cf. A283435, A286892, A287020, A287021, A287022, A287377, A287383, A287384.
%K A287378 nonn,tabl
%O A287378 0,10
%A A287378 _María Merino_, Imanol Unanue, May 24 2017