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 A287377 #24 Apr 10 2020 01:39:42
%S A287377 1,1,1,1,1,1,1,1,1,22680,1,1,5040,3742560,4540536000,1,1,113400,
%T A287377 851370480,6518191680000,54111175679736000
%N A287377 Triangle read by rows: T(n,m) is the number of inequivalent n X m matrices under action of the Klein group, with one-seventh each of 1's, 2's, 3's, 4's, 5's, 6's and 7's (ordered occurrences rounded up/down if n*m != 0 mod 7).
%C A287377 Computed using Polya's enumeration theorem for coloring.
%H A287377 María Merino, <a href="/A287377/b287377.txt">Rows n=0..36 of triangle, flattened</a>
%H A287377 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 A287377 g(x1,x2,x3,x4,x5,x6,x7)=(y1^(m*n) + 3*y2^(m*n/2))/4 for even n and m;
%F A287377 (y1^(m*n) + y1^n*y2^((m*n-m)/2) + 2*y2^(m*n/2))/4 for odd n and even m;
%F A287377 (y1^(m*n) + y1^m*y2^((m*n-n)/2) + 2*y2^(m*n/2))/4 for even n and odd m; (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 coefficient correspond to y1=Sum_{i=1..7} x_i, y2=Sum_{i=1..7} x_i^2, and occurrences of numbers are ceiling(m*n/7) for the first k numbers and floor(m*n/7) for the last (7-k) numbers, if m*n = k mod 7.
%e A287377 For n = 4 and m = 2 the T(4,2) = 5040 solutions are colorings of 4 X 2 matrices in 7 colors inequivalent under the action of the Klein group with exactly 2, 1, 1, 1, 1, 1, 1 occurrences of each color (coefficient of x1^2 x2^1 x3^1 x4^1 x5^1 x6^1 x7^1).
%e A287377 Triangle begins:
%e A287377 ==============================================================
%e A287377 n\m | 0 1 2 3 4 5
%e A287377 ----|---------------------------------------------------------
%e A287377 0 | 1
%e A287377 1 | 1 1
%e A287377 2 | 1 1 1
%e A287377 3 | 1 1 1 22680
%e A287377 4 | 1 1 5040 3742560 4540536000
%e A287377 5 | 1 1 113400 851370480 6518191680000 54111175679736000
%Y A287377 Cf. A283435, A286892, A287020, A287021, A287022, A287378, A287383, A287384.
%K A287377 nonn,tabl
%O A287377 0,10
%A A287377 _María Merino_, Imanol Unanue, May 24 2017