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 A358050 #48 Oct 31 2022 15:24:16
%S A358050 1,1,0,1,2,0,1,4,3,0,1,6,16,4,0,1,8,39,64,5,0,1,10,72,258,256,6,0,1,
%T A358050 12,115,664,1719,1024,7,0,1,14,168,1360,6184,11496,4096,8,0,1,16,231,
%U A358050 2424,16265,57888,77052,16384,9,0,1,18,304,3934,35400,195660,543544,517194,65536,10,0
%N A358050 Square array T(n,k), n >= 0, k >= 0, read by antidiagonals downwards, where T(n,k) = Sum_{j=0..n} binomial(k*j,j) * binomial(k*(n-j),n-j).
%F A358050 T(n,k) = Sum_{j=0..n} (k-1)^(n-j) * binomial(k*n+1,j).
%F A358050 T(n,k) = Sum_{j=0..n} k^(n-j) * binomial((k-1)*n+j,j).
%e A358050 Square array begins:
%e A358050 1, 1, 1, 1, 1, 1, ...
%e A358050 0, 2, 4, 6, 8, 10, ...
%e A358050 0, 3, 16, 39, 72, 115, ...
%e A358050 0, 4, 64, 258, 664, 1360, ...
%e A358050 0, 5, 256, 1719, 6184, 16265, ...
%e A358050 0, 6, 1024, 11496, 57888, 195660, ...
%o A358050 (PARI) T(n, k) = sum(j=0, n, binomial(k*j, j)*binomial(k*(n-j), n-j));
%o A358050 (PARI) T(n, k) = sum(j=0, n, (k-1)^(n-j)*binomial(k*n+1, j));
%o A358050 (PARI) T(n, k) = sum(j=0, n, k^(n-j)*binomial((k-1)*n+j, j));
%Y A358050 Column k=0-7 give: A000007, A001477(n+1), A000302, A006256, A078995, A079678, A079679, A079563.
%Y A358050 Main diagonal gives A358145.
%Y A358050 Cf. A358146.
%K A358050 nonn,tabl
%O A358050 0,5
%A A358050 _Seiichi Manyama_, Oct 31 2022