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 A337464 #21 Apr 29 2021 04:35:40
%S A337464 1,1,6,1,5,30,1,4,11,140,1,3,-6,-29,630,1,2,-21,-120,-365,2772,1,1,
%T A337464 -34,-139,-266,-1409,12012,1,0,-45,-92,531,2520,-155,51480,1,-1,-54,
%U A337464 15,1654,6489,17380,29485,218790,1,-2,-61,176,2755,4828,-9723,-13104,170035,923780
%N A337464 Square array T(n,k), n >= 0, k >= 0, read by antidiagonals, where column k is the expansion of sqrt(2 / ( (1+2*(k-4)*x+((k+4)*x)^2) * (1-(k+4)*x+sqrt(1+2*(k-4)*x+((k+4)*x)^2)) )).
%H A337464 Seiichi Manyama, <a href="/A337464/b337464.txt">Antidiagonals n = 0..139, flattened</a>
%F A337464 T(n,k) = Sum_{j=0..n} (-k)^(n-j) * binomial(2*j,j) * binomial(2*n+1,2*j).
%F A337464 T(0,k) = 1, T(1,k) = 6-k and n * (2*n+1) * (4*n-3) * T(n,k) = (4*n-1) * (-4*(k-4)*n^2+2*(k-4)*n+k-2) * T(n-1,k) - (k+4)^2 * (n-1) * (2*n-1) * (4*n+1) * T(n-2,k) for n > 1. - _Seiichi Manyama_, Aug 29 2020
%e A337464 Square array begins:
%e A337464 1, 1, 1, 1, 1, 1, ...
%e A337464 6, 5, 4, 3, 2, 1, ...
%e A337464 30, 11, -6, -21, -34, -45, ...
%e A337464 140, -29, -120, -139, -92, 15, ...
%e A337464 630, -365, -266, 531, 1654, 2755, ...
%e A337464 2772, -1409, 2520, 6489, 4828, -5853, ...
%t A337464 T[n_, k_] := Sum[If[k == n-j == 0, 1, (-k)^(n-j)] * Binomial[2*j, j] * Binomial[2*n+1, 2*j], {j, 0, n}]; Table[T[k, n - k], {n, 0, 9}, {k, 0, n}] // Flatten (* _Amiram Eldar_, Apr 29 2021 *)
%o A337464 (PARI) {T(n, k) = sum(j=0, n, (-k)^(n-j)*binomial(2*j, j)*binomial(2*n+1, 2*j))}
%Y A337464 Columns k=0..4 give A002457, A337394, A337466, A337467, A337397.
%Y A337464 Main diagonal gives A337465.
%Y A337464 Cf. A337369, A337419.
%K A337464 sign,tabl
%O A337464 0,3
%A A337464 _Seiichi Manyama_, Aug 28 2020