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 A337467 #20 Apr 29 2021 04:32:33
%S A337467 1,3,-21,-139,531,6489,-9723,-292293,-135117,12514313,29905809,
%T A337467 -501239553,-2310673379,18245192679,140574917259,-562805403867,
%U A337467 -7557237645741,11275709877369,371974318253601,201852054629631,-16932135947326551,-42530838930147813,709138646702505999
%N A337467 Expansion of sqrt(2 / ( (1-2*x+49*x^2) * (1-7*x+sqrt(1-2*x+49*x^2)) )).
%H A337467 Seiichi Manyama, <a href="/A337467/b337467.txt">Table of n, a(n) for n = 0..1000</a>
%F A337467 a(n) = Sum_{k=0..n} (-3)^(n-k) * binomial(2*k,k) * binomial(2*n+1,2*k).
%F A337467 a(0) = 1, a(1) = 3 and n * (2*n+1) * (4*n-3) * a(n) = (4*n-1) * (4*n^2-2*n+1) * a(n-1) - 49 * (n-1) * (2*n-1) * (4*n+1) * a(n-2) for n > 1. - _Seiichi Manyama_, Aug 29 2020
%t A337467 a[n_] := Sum[(-3)^(n-k) * Binomial[2*k, k] * Binomial[2*n+1, 2*k], {k, 0, n}]; Array[a, 23, 0] (* _Amiram Eldar_, Apr 29 2021 *)
%o A337467 (PARI) N=40; x='x+O('x^N); Vec(sqrt(2/((1-2*x+49*x^2)*(1-7*x+sqrt(1-2*x+49*x^2)))))
%o A337467 (PARI) {a(n) = sum(k=0, n, (-3)^(n-k)*binomial(2*k, k)*binomial(2*n+1, 2*k))}
%Y A337467 Column k=3 of A337464.
%Y A337467 Cf. A245927, A337422.
%K A337467 sign
%O A337467 0,2
%A A337467 _Seiichi Manyama_, Aug 28 2020