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 A241956 #31 May 02 2022 10:23:43
%S A241956 2,3,3,4,7,4,5,13,13,5,6,22,36,22,6,7,34,87,87,34,7,8,50,190,317,190,
%T A241956 50,8,9,70,386,1053,1053,386,70,9,10,95,734,3250,5624,3250,734,95,10,
%U A241956 11,125,1324,9343,28576,28576,9343,1324,125,11
%N A241956 Number of inequivalent m X n binary matrices, where equivalence means permutations of rows or columns. Presented in diagonal order, with (m,n)=(1,1), (1,2), (2,1), (1,3), (2,2), (3,1), ... .
%C A241956 Same as A028657 without first row and column.
%H A241956 Alois P. Heinz, <a href="/A241956/b241956.txt">Antidiagonals m = 1..45, flattened</a>
%H A241956 Adalbert Kerber, Applied Finite Group Actions, second edition, Springer-Verlag, (1999). See table under Corollary 2.3.1 on page 68.
%H A241956 Various authors, <a href="http://math.stackexchange.com/questions/22159/#881965">How many n-by-m binary matrices are there up to row and column permutations</a>
%H A241956 <a href="/index/Mat#inequiv">Index to number of inequivalent matrices modulo permutation of rows and columns</a>
%e A241956 The array begins:
%e A241956 2 3 4 5 6 7 8 9 ...
%e A241956 3 7 13 22 34 50 70 95 ...
%e A241956 4 13 36 87 190 386 734 1324 ...
%e A241956 5 22 87 317 1053 3250 9343 25207 ...
%e A241956 6 34 190 1053 5624 28576 136758 613894 ...
%e A241956 7 50 386 3250 28576 251610 2141733 17256831 ...
%e A241956 8 70 734 9343 136758 2141733 33642660 508147108 ...
%e A241956 9 95 1324 25207 613894 17256831 508147108 14685630688 ...
%e A241956 (cf. A028657).
%p A241956 b:= proc(n, i) b(n, i):= `if`(n=0, [[]], `if`(i<1, [], [seq(map(
%p A241956 p->`if`(j=0, p, [p[], [i, j]]), b(n-i*j, i-1))[], j=0..n/i)]))
%p A241956 end:
%p A241956 g:= proc(n, k) option remember; add(add(2^add(add(i[2]*j[2]*
%p A241956 igcd(i[1], j[1]), j=t), i=s) /mul(i[1]^i[2]*i[2]!, i=s)
%p A241956 /mul(i[1]^i[2]*i[2]!, i=t), t=b(n+k$2)), s=b(n$2))
%p A241956 end:
%p A241956 A:= (m, n)-> g(min(m, n), abs(m-n)):
%p A241956 seq(seq(A(m, 1+d-m), m=1..d), d=1..12); # _Alois P. Heinz_, Aug 13 2014
%t A241956 b[n_, i_] := b[n, i] = If[n == 0, {0}, If[i < 1, {}, Union[Flatten[Table[ Function[{p}, p + j*x^i] /@ b[n - i*j, i - 1], {j, 0, n/i}]]]]];
%t A241956 g[n_, k_] := g[n, k] = Sum[Sum[2^Sum[Sum[GCD[i, j]*Coefficient[s, x, i]* Coefficient[t, x, j], {j, 1, Exponent[t, x]}], {i, 1, Exponent[s, x]}]/ Product[i^Coefficient[s, x, i]*Coefficient[s, x, i]!, {i, 1, Exponent[s, x]}]/Product[i^Coefficient[t, x, i]*Coefficient[t, x, i]!, {i, 1, Exponent[t, x]}], {t, b[n + k, n + k]}], {s, b[n, n]}];
%t A241956 A[n_, k_] := g[Min[n, k], Abs[n - k]];
%t A241956 Table[A[n - k + 1, k], {n, 1, 12}, {k, 1, n}] // Flatten (* _Jean-François Alcover_, Dec 09 2019, after _Alois P. Heinz_ in A028657 *)
%Y A241956 Cf. A002724.
%K A241956 nonn,tabl
%O A241956 1,1
%A A241956 _Don Knuth_, Aug 09 2014