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 A358363 #20 Nov 15 2023 03:12:34
%S A358363 1,12,196,3120,50020,799536,12799632,204724416,3276326820,52413049520,
%T A358363 838703348496,13418125153472,214703825630736,3435088134123200,
%U A358363 54963617747611200,879389273444524800,14070604335190692900,225124668703739770800,3602061930346132909200
%N A358363 a(n) = 16^n * Sum_{k=0..n} (-1)^k*binomial(1/2, k)^2.
%F A358363 a(n) = (64*(2*n - 3)^2*a(n - 2) + 12*(4*n - 3)*a(n - 1)) / n^2.
%F A358363 G.f.: hypergeom([-1/2, -1/2], [1], -16*x)/(1 - 16*x).
%F A358363 a(n) ~ sqrt(Pi) * 2^(4*n + 5/2) / Gamma(1/4)^2. - _Vaclav Kotesovec_, Nov 14 2023
%p A358363 a := n -> 16^n*add((-1)^k*binomial(1/2, k)^2, k = 0..n):
%p A358363 seq(a(n), n = 0..18);
%t A358363 a[n_] := 16^n * Sum[(-1)^k*Binomial[1/2, k]^2, {k, 0, n}]; Array[a, 19, 0] (* _Amiram Eldar_, Nov 12 2022 *)
%Y A358363 Cf. A358362, A358364, A358365, A367331.
%K A358363 nonn
%O A358363 0,2
%A A358363 _Peter Luschny_, Nov 12 2022