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 A307039 #24 May 20 2021 04:44:58
%S A307039 1,1,0,1,1,0,1,1,0,0,1,1,1,-2,0,1,1,1,0,-4,0,1,1,1,1,-3,-4,0,1,1,1,1,
%T A307039 0,-9,0,0,1,1,1,1,1,-4,-18,8,0,1,1,1,1,1,0,-14,-27,16,0,1,1,1,1,1,1,
%U A307039 -5,-34,-27,16,0,1,1,1,1,1,1,0,-20,-68,0,0,0,1,1,1,1,1,1,1,-6,-55,-116,81,-32,0
%N A307039 Square array A(n,k), n >= 0, k >= 1, read by antidiagonals, where column k is the expansion of g.f. ((1-x)^(k-1))/((1-x)^k+x^k).
%H A307039 Seiichi Manyama, <a href="/A307039/b307039.txt">Antidiagonals n = 0..139, flattened</a>
%F A307039 A(n,k) = Sum_{j=0..floor(n/k)} (-1)^j * binomial(n,k*j).
%e A307039 Square array begins:
%e A307039 1, 1, 1, 1, 1, 1, 1, 1, ...
%e A307039 0, 1, 1, 1, 1, 1, 1, 1, ...
%e A307039 0, 0, 1, 1, 1, 1, 1, 1, ...
%e A307039 0, -2, 0, 1, 1, 1, 1, 1, ...
%e A307039 0, -4, -3, 0, 1, 1, 1, 1, ...
%e A307039 0, 0, -18, -14, -5, 0, 1, 1, ...
%e A307039 0, 8, -27, -34, -20, -6, 0, 1, ...
%e A307039 0, 16, -27, -68, -55, -27, -7, 0, ...
%e A307039 0, 16, 0, -116, -125, -83, -35, -8, ...
%t A307039 T[n_, k_] := Sum[(-1)^j * Binomial[n, k*j], {j, 0, Floor[n/k]}]; Table[T[n-k, k], {n, 0, 13}, {k, n, 1, -1}] // Flatten (* _Amiram Eldar_, May 20 2021 *)
%Y A307039 Columns 1-9 give A000007, A146559, A057681, A099586, A289306, A307040, A307041, A307044, A307045.
%Y A307039 Cf. A306846, A306914.
%K A307039 sign,tabl,look
%O A307039 0,14
%A A307039 _Seiichi Manyama_, Mar 21 2019