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 A330843 #44 May 05 2021 01:51:45
%S A330843 1,1,0,1,2,-2,1,4,6,0,1,6,30,20,6,1,8,70,256,70,0,1,10,126,924,2310,
%T A330843 252,-20,1,12,198,2240,12870,21504,924,0,1,14,286,4420,41990,184756,
%U A330843 204204,3432,70,1,16,390,7680,104006,811008,2704156,1966080,12870,0
%N A330843 Square array T(n,k) = [x^n] ((1+x)^(k+1) / (1-x)^(k-1))^n, n>=0, k>=0, read by descending antidiagonals.
%H A330843 Seiichi Manyama, <a href="/A330843/b330843.txt">Antidiagonals n = 0..139, flattened</a>
%F A330843 T(n,k) = Sum_{j=0..n} binomial((k+1)*n,j) * binomial(k*n-j-1,n-j).
%F A330843 T(n,k) = 1/n! * ((k+1)*n)!/Gamma(1 + (k+1)*n/2) * Gamma(1 + (k-1)*n/2)/((k-1)*n)!.
%e A330843 Square array begins:
%e A330843 1, 1, 1, 1, 1, 1, ...
%e A330843 0, 2, 4, 6, 8, 10, ...
%e A330843 -2, 6, 30, 70, 126, 198, ...
%e A330843 0, 20, 256, 924, 2240, 4420, ...
%e A330843 6, 70, 2310, 12870, 41990, 104006, ...
%e A330843 0, 252, 21504, 184756, 811008, 2521260, ...
%t A330843 T[n_, k_] := Sum[Binomial[(k + 1)*n, j] * Binomial[k*n - j - 1, n - j], {j, 0, n}]; Table[T[k, n - k], {n, 0, 9}, {k, 0, n}] // Flatten (* _Amiram Eldar_, May 05 2021 *)
%Y A330843 Columns k=1..7 give A000984, A091527, A001448, A262732, A211419, A262733, A211421.
%Y A330843 Main diagonal is A332231.
%K A330843 sign,tabl
%O A330843 0,5
%A A330843 _Seiichi Manyama_, Feb 07 2020