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 A307090 #20 May 20 2021 04:44:44
%S A307090 1,1,1,1,1,1,1,1,1,1,1,1,0,1,1,1,1,-2,-2,1,1,1,1,-5,-8,-5,1,1,1,1,-9,
%T A307090 -17,-17,-9,1,1,1,1,-14,-29,-34,-29,-14,1,1,1,1,-20,-44,-54,-54,-44,
%U A307090 -20,1,1,1,1,-27,-62,-74,-74,-74,-62,-27,1,1,1,1,-35,-83,-90,-74,-74,-90,-83,-35,1,1
%N A307090 Number triangle T(n,k) = Sum_{j=0..n-k} (-1)^j * binomial(k,2*j) * binomial(n-k,2*j).
%H A307090 Seiichi Manyama, <a href="/A307090/b307090.txt">Rows n = 0..139, flattened</a>
%e A307090 Triangle begins:
%e A307090 n\k | 0 1 2 3 4 5 6 7 8
%e A307090 ----+-------------------------------------
%e A307090 0 | 1;
%e A307090 1 | 1, 1;
%e A307090 2 | 1, 1, 1;
%e A307090 3 | 1, 1, 1, 1;
%e A307090 4 | 1, 1, 0, 1, 1;
%e A307090 5 | 1, 1, -2, -2, 1, 1;
%e A307090 6 | 1, 1, -5, -8, -5, 1, 1;
%e A307090 7 | 1, 1, -9, -17, -17, -9, 1, 1;
%e A307090 8 | 1, 1, -14, -29, -34, -29, -14, 1, 1;
%t A307090 T[n_, k_] := Sum[(-1)^j * Binomial[k, 2*j] * Binomial[n - k, 2*j], {j, 0, n - k}]; Table[T[n, k], {n, 0, 11}, {k, 0, n}] // Flatten (* _Amiram Eldar_, May 20 2021 *)
%Y A307090 Row sums give A099587(n+1).
%Y A307090 T(2*n,n) gives A307091.
%Y A307090 Cf. A007318, A098593, A119326, A119335.
%K A307090 sign,tabl,look
%O A307090 0,18
%A A307090 _Seiichi Manyama_, Mar 24 2019