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 A337397 #19 Jul 24 2021 12:35:02
%S A337397 1,2,-34,-92,1654,4828,-88724,-268088,4984486,15361708,-287691196,
%T A337397 -898052872,16901635516,53234639768,-1005474931816,-3187958034544,
%U A337397 60375963282182,192405594166988,-3651655920615596,-11684176213422568,222132094724096852,713091439789994824,-13575872676384218776
%N A337397 Expansion of sqrt(2 / ( (1+64*x^2) * (1-8*x+sqrt(1+64*x^2)) )).
%H A337397 Seiichi Manyama, <a href="/A337397/b337397.txt">Table of n, a(n) for n = 0..1000</a>
%F A337397 a(n) = Sum_{k=0..n} (-4)^(n-k) * binomial(2*k,k) * binomial(2*n+1,2*k).
%F A337397 a(0) = 1, a(1) = 2 and n * (2*n+1) * (4*n-3) * a(n) = (4*n-1) * 2 * a(n-1) - 64 * (n-1) * (2*n-1) * (4*n+1) * a(n-2) for n > 1. - _Seiichi Manyama_, Aug 29 2020
%t A337397 a[n_] := Sum[(-4)^(n - k) * Binomial[2*k, k] * Binomial[2*n + 1, 2*k], {k, 0, n}]; Array[a, 23, 0] (* _Amiram Eldar_, Aug 26 2020 *)
%t A337397 CoefficientList[Series[Sqrt[2/((1+64x^2)(1-8x+Sqrt[1+64x^2]))],{x,0,30}],x] (* _Harvey P. Dale_, Jul 24 2021 *)
%o A337397 (PARI) N=40; x='x+O('x^N); Vec(sqrt(2/((1+64*x^2)*(1-8*x+sqrt(1+64*x^2)))))
%o A337397 (PARI) {a(n) = sum(k=0, n, (-4)^(n-k)*binomial(2*k, k)*binomial(2*n+1, 2*k))}
%Y A337397 Column k=4 of A337464.
%Y A337397 Cf. A002458, A193618, A337396.
%K A337397 sign
%O A337397 0,2
%A A337397 _Seiichi Manyama_, Aug 26 2020