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 A333991 #21 Sep 05 2020 13:13:50
%S A333991 1,0,-7,64,-527,3776,-7199,-712704,28545857,-881543168,25615822601,
%T A333991 -733594255360,20859188600881,-580152163418112,15048530008948913,
%U A333991 -311489672222081024,713562283940993281,511135051171610230784,-48010258775057340355559,3439412411849176925601792
%N A333991 a(n) = Sum_{k=0..n} (-n)^k * binomial(2*n,2*k).
%H A333991 Seiichi Manyama, <a href="/A333991/b333991.txt">Table of n, a(n) for n = 0..386</a>
%F A333991 From _Vaclav Kotesovec_, Sep 05 2020: (Start)
%F A333991 a(n) = hypergeometric2F1(1/2 - n, -n, 1/2, -n).
%F A333991 a(n) = (1 + i*sqrt(n))^(2*n)/2 + (1 - i*sqrt(n))^(2*n)/2, where i is the imaginary unit.
%F A333991 a(n) = cos(2*n*arctan(sqrt(n))) * (n + 1)^n. (End)
%t A333991 a[0] = 1; a[n_] := Sum[(-n)^k * Binomial[2*n, 2*k], {k, 0, n}]; Array[a, 20, 0] (* _Amiram Eldar_, Sep 04 2020 *)
%t A333991 Table[Hypergeometric2F1[1/2 - n, -n, 1/2, -n], {n, 0, 20}] (* _Vaclav Kotesovec_, Sep 05 2020 *)
%t A333991 Table[Cos[2*n*ArcTan[Sqrt[n]]] * (n + 1)^n, {n, 0, 20}] // Round (* _Vaclav Kotesovec_, Sep 05 2020 *)
%o A333991 (PARI) {a(n) = sum(k=0, n, (-n)^k*binomial(2*n, 2*k))}
%Y A333991 Main diagonal of A333989.
%Y A333991 Cf. A065440, A333990.
%K A333991 sign
%O A333991 0,3
%A A333991 _Seiichi Manyama_, Sep 04 2020