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 A337396 #22 Aug 29 2020 01:54:16
%S A337396 1,-2,-26,76,1222,-3772,-64676,203992,3607622,-11510636,-207302156,
%T A337396 666187432,12142184476,-39211413464,-720760216328,2335857124016,
%U A337396 43208062233158,-140406756766796,-2609918906614652,8498967890177416,158596941629422132,-517334728427373704,-9684521991498517112
%N A337396 Expansion of sqrt((1-8*x+sqrt(1+64*x^2)) / (2 * (1+64*x^2))).
%H A337396 Seiichi Manyama, <a href="/A337396/b337396.txt">Table of n, a(n) for n = 0..1000</a>
%F A337396 a(n) = Sum_{k=0..n} (-4)^(n-k) * binomial(2*k,k) * binomial(2*n,2*k).
%F A337396 a(0) = 1, a(1) = -2 and n * (2*n-1) * (4*n-5) * a(n) = (4*n-3) * 2 * a(n-1) - 64 * (n-1) * (2*n-3) * (4*n-1) * a(n-2) for n > 1. - _Seiichi Manyama_, Aug 28 2020
%t A337396 a[n_] := Sum[(-4)^(n - k) * Binomial[2*k, k] * Binomial[2*n, 2*k], {k, 0, n}]; Array[a, 23, 0] (* _Amiram Eldar_, Aug 26 2020 *)
%o A337396 (PARI) N=40; x='x+O('x^N); Vec(sqrt((1-8*x+sqrt(1+64*x^2))/(2*(1+64*x^2))))
%o A337396 (PARI) {a(n) = sum(k=0, n, (-4)^(n-k)*binomial(2*k, k)*binomial(2*n, 2*k))}
%Y A337396 Column k=4 of A337419.
%Y A337396 Cf. A001448, A193619, A337397.
%K A337396 sign
%O A337396 0,2
%A A337396 _Seiichi Manyama_, Aug 26 2020