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 A328807 #25 May 06 2021 03:16:16
%S A328807 1,1,3,1,3,8,1,3,9,20,1,3,11,27,48,1,3,15,45,81,112,1,3,23,93,195,243,
%T A328807 256,1,3,39,225,639,873,729,576,1,3,71,597,2583,4653,3989,2187,1280,1,
%U A328807 3,135,1665,11991,32133,35169,18483,6561,2816
%N A328807 Square array T(n,k), n >= 0, k >= 0, read by antidiagonals, where T(n,k) is Sum_{i=0..n} binomial(n,i)*Sum_{j=0..i} binomial(i,j)^k.
%C A328807 T(n,k) is the constant term in the expansion of (1 + Product_{j=1..k-1} (1 + x_j) + Product_{j=1..k-1} (1 + 1/x_j))^n for k > 0.
%C A328807 For fixed k > 0 is T(n,k) ~ (2^k + 1)^(n + (k-1)/2) / (2^((k-1)^2/2) * sqrt(k) * (Pi*n)^((k-1)/2)). - _Vaclav Kotesovec_, Oct 28 2019
%H A328807 Seiichi Manyama, <a href="/A328807/b328807.txt">Antidiagonals n = 0..100, flattened</a>
%e A328807 Square array begins:
%e A328807 1, 1, 1, 1, 1, 1, ...
%e A328807 3, 3, 3, 3, 3, 3, ...
%e A328807 8, 9, 11, 15, 23, 39, ...
%e A328807 20, 27, 45, 93, 225, 597, ...
%e A328807 48, 81, 195, 639, 2583, 11991, ...
%e A328807 112, 243, 873, 4653, 32133, 260613, ...
%t A328807 T[n_, k_] := Sum[Binomial[n, i] * Sum[Binomial[i, j]^k, {j, 0, i}], {i, 0, n}]; Table[T[k, n - k], {n, 0, 9}, {k, 0, n}] // Flatten (* _Amiram Eldar_, May 06 2021 *)
%Y A328807 Columns k=0..5 give A001792, A000244, A026375, A002893, A328808, A328809.
%Y A328807 Main diagonal gives A328810.
%Y A328807 Cf. A309010, A328747, A328748.
%K A328807 nonn,tabl
%O A328807 0,3
%A A328807 _Seiichi Manyama_, Oct 28 2019