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 A363349 #7 May 30 2023 14:10:44
%S A363349 1,1,1,1,1,1,1,1,2,1,1,1,3,2,1,1,1,4,4,3,1,1,1,5,7,8,3,1,1,1,6,11,19,
%T A363349 10,4,1,1,1,7,16,41,32,16,4,1,1,1,8,23,81,101,68,20,5,1,1,1,9,31,153,
%U A363349 299,301,114,29,5,1,1,1,10,41,273,849,1358,757,210,35,6,1
%N A363349 Array read by antidiagonals: T(n,k) is the number of equivalence classes of n X k binary matrices under permutation of rows and columns and complementation of columns.
%C A363349 T(n,k) is also the number of equivalence classes of n X k binary matrices with an even number of 1's in each column under permutation of rows and columns.
%H A363349 Andrew Howroyd, <a href="/A363349/b363349.txt">Table of n, a(n) for n = 0..1325</a>
%H A363349 M. A. Harrison, <a href="http://dx.doi.org/10.1109/T-C.1973.223649">On the number of classes of binary matrices</a>, IEEE Trans. Computers, 22 (1973), 1048-1051.
%H A363349 M. A. Harrison, <a href="/A000711/a000711.pdf">On the number of classes of binary matrices</a>, IEEE Transactions on Computers, C-22.12 (1973), 1048-1052. (Annotated scanned copy)
%e A363349 Array begins:
%e A363349 ======================================================
%e A363349 n/k| 0 1 2 3 4 5 6 7 8 ...
%e A363349 ---+--------------------------------------------------
%e A363349 0 | 1 1 1 1 1 1 1 1 1 ...
%e A363349 1 | 1 1 1 1 1 1 1 1 1 ...
%e A363349 2 | 1 2 3 4 5 6 7 8 9 ...
%e A363349 3 | 1 2 4 7 11 16 23 31 41 ...
%e A363349 4 | 1 3 8 19 41 81 153 273 468 ...
%e A363349 5 | 1 3 10 32 101 299 849 2290 5901 ...
%e A363349 6 | 1 4 16 68 301 1358 6128 27008 114763 ...
%e A363349 7 | 1 4 20 114 757 5567 43534 343656 2645494 ...
%e A363349 8 | 1 5 29 210 1981 23350 319119 4633380 67013431 ...
%e A363349 ...
%o A363349 (PARI) \\ Compare A028657.
%o A363349 permcount(v) = {my(m=1, s=0, k=0, t); for(i=1, #v, t=v[i]; k=if(i>1&&t==v[i-1], k+1, 1); m*=t*k; s+=t); s!/m}
%o A363349 K(q, t)={sum(j=1, #q, gcd(t, q[j]))}
%o A363349 T(n, k)={if(n==0, 1, my(s=0); forpart(q=n, my(e=1<<valuation(Vec(q), 2)); s+=permcount(q)*polcoef(exp(sum(t=1, k, 2^(K(q, t)-(t%e==0))/t*x^t) + O(x*x^k)), k)); s/n!)}
%Y A363349 A259344 is the same array without the first row and column read by upward antidiagonals.
%Y A363349 Columns k=0..6 are A000012, A004526(n+2), A005232, A006381, A006382, A056204, A056205.
%Y A363349 Rows n=2..4 are A000027(n+1), A000601, A006380.
%Y A363349 Main diagonal is A006383.
%Y A363349 Cf. A028657, A241956, A362905.
%K A363349 nonn,tabl
%O A363349 0,9
%A A363349 _Andrew Howroyd_, May 28 2023