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 A358362 #18 Nov 15 2023 03:12:00
%S A358362 1,12,228,3248,56868,846384,14395920,218556096,3662534436,56236646576,
%T A358362 933921124752,14445103689408,238434118702864,3706773418885824,
%U A358362 60917716297733184,950622015752780544,15571249887287040804,243694280206569964464,3981466564018425521424
%N A358362 a(n) = 16^n * Sum_{k=0..n} (-1)^k*binomial(-1/2, k)^2.
%F A358362 a(n) = (64*(2*n - 1)^2*a(n - 2) + (16*n - 4)*a(n - 1)) / n^2.
%F A358362 G.f.: hypergeom([1/2, 1/2], [1], -16*x)/(16*x - 1).
%F A358362 G.f.: 2*EllipticK(4*I*sqrt(x))/(Pi*(1 - 16*x)).
%F A358362 a(n) ~ A014549 * 2^(4*n). - _Vaclav Kotesovec_, Nov 14 2023
%p A358362 a := n -> 16^n*add((-1)^k*binomial(-1/2, k)^2, k = 0..n):
%p A358362 seq(a(n), n = 0..19);
%t A358362 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 A358362 Cf. A358363, A358364, A358365, A367330.
%K A358362 nonn
%O A358362 0,2
%A A358362 _Peter Luschny_, Nov 12 2022