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 A328748 #37 May 06 2021 03:16:07
%S A328748 1,1,0,1,0,-1,1,0,0,2,1,0,2,0,-3,1,0,6,0,0,4,1,0,14,12,6,0,-5,1,0,30,
%T A328748 72,90,0,0,6,1,0,62,300,882,360,20,0,-7,1,0,126,1080,6690,8400,2040,0,
%U A328748 0,8,1,0,254,3612,44706,124920,95180,10080,70,0,-9
%N A328748 Square array T(n,k), n >= 0, k >= 0, read by antidiagonals, where T(n,k) is Sum_{i=0..n} (-2)^(n-i)*binomial(n,i)*Sum_{j=0..i} binomial(i,j)^k.
%C A328748 T(n,k) is the constant term in the expansion of (-2 + Product_{j=1..k-1} (1 + x_j) + Product_{j=1..k-1} (1 + 1/x_j))^n for k > 0.
%H A328748 Seiichi Manyama, <a href="/A328748/b328748.txt">Antidiagonals n = 0..100, flattened</a>
%e A328748 Square array begins:
%e A328748 1, 1, 1, 1, 1, 1, ...
%e A328748 0, 0, 0, 0, 0, 0, ...
%e A328748 -1, 0, 2, 6, 14, 30, ...
%e A328748 2, 0, 0, 12, 72, 300, ...
%e A328748 -3, 0, 6, 90, 882, 6690, ...
%e A328748 4, 0, 0, 360, 8400, 124920, ...
%t A328748 T[n_, k_] := Sum[(-2)^(n-i) * Binomial[n, i] * Sum[Binomial[i, j]^k, {j, 0, i}], {i, 0, n}]; Table[T[k, n - k], {n, 0, 10}, {k, 0, n}] // Flatten (* _Amiram Eldar_, May 06 2021 *)
%Y A328748 Columns k=0..5 give A097141(n+1), A000007, A126869, A002898, A328735, A328751.
%Y A328748 T(n,n+1) gives A328814.
%Y A328748 Cf. A309010, A328747, A328807.
%K A328748 sign,tabl
%O A328748 0,10
%A A328748 _Seiichi Manyama_, Oct 27 2019