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 A337422 #23 Aug 29 2020 02:18:19
%S A337422 1,-1,-21,-7,739,1629,-26859,-118329,922419,6886397,-27414191,
%T A337422 -358533429,539620621,17229485987,8782716411,-769962297447,
%U A337422 -1897237412973,31786556599917,149610560086113,-1182765435388341,-9268347520205991,37049669347266471,505738623506722431
%N A337422 Expansion of sqrt((1-7*x+sqrt(1-2*x+49*x^2)) / (2 * (1-2*x+49*x^2))).
%H A337422 Seiichi Manyama, <a href="/A337422/b337422.txt">Table of n, a(n) for n = 0..1000</a>
%F A337422 a(n) = Sum_{k=0..n} (-3)^(n-k) * binomial(2*k,k) * binomial(2*n,2*k).
%F A337422 a(0) = 1, a(1) = -1 and n * (2*n-1) * (4*n-5) * a(n) = (4*n-3) * (4*n^2-6*n+3) * a(n-1) - 49 * (n-1) * (2*n-3) * (4*n-1) * a(n-2) for n > 1. - _Seiichi Manyama_, Aug 28 2020
%t A337422 a[n_] := Sum[(-3)^(n - k) * Binomial[2*k, k] * Binomial[2*n, 2*k], {k, 0, n}]; Array[a, 23, 0] (* _Amiram Eldar_, Aug 27 2020 *)
%o A337422 (PARI) N=40; x='x+O('x^N); Vec(sqrt((1-7*x+sqrt(1-2*x+49*x^2))/(2*(1-2*x+49*x^2))))
%o A337422 (PARI) {a(n) = sum(k=0, n, (-3)^(n-k)*binomial(2*k, k)*binomial(2*n, 2*k))}
%Y A337422 Column k=3 of A337419.
%Y A337422 Cf. A245926.
%K A337422 sign
%O A337422 0,3
%A A337422 _Seiichi Manyama_, Aug 27 2020