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 A333990 #22 Sep 05 2020 03:42:10
%S A333990 1,2,17,208,3281,62976,1419193,36643328,1064876737,34359869440,
%T A333990 1217844546401,47005113741312,1961498610274321,87961440484327424,
%U A333990 4217109422614386761,215187913985734475776,11641533109203575871233,665430291591787349803008,40065760383961956327231409
%N A333990 a(n) = Sum_{k=0..n} n^k * binomial(2*n,2*k).
%H A333990 Seiichi Manyama, <a href="/A333990/b333990.txt">Table of n, a(n) for n = 0..381</a>
%F A333990 From _Vaclav Kotesovec_, Sep 05 2020: (Start)
%F A333990 a(n) = hypergeometric2F1(1/2 - n, -n, 1/2, n).
%F A333990 a(n) = (1 + sqrt(n))^(2*n)/2 + (1 - sqrt(n))^(2*n)/2.
%F A333990 a(n) ~ exp(2*sqrt(n) - 1) * n^n / 2 * (1 + 2/(3*sqrt(n))). (End)
%t A333990 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 A333990 Table[Hypergeometric2F1[1/2 - n, -n, 1/2, n], {n, 0, 20}] (* _Vaclav Kotesovec_, Sep 05 2020 *)
%o A333990 (PARI) {a(n) = sum(k=0, n, n^k*binomial(2*n, 2*k))}
%Y A333990 Main diagonal of A333988.
%Y A333990 Cf. A333991.
%K A333990 nonn
%O A333990 0,2
%A A333990 _Seiichi Manyama_, Sep 04 2020