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 A368888 #9 Jan 09 2024 08:45:51
%S A368888 1,1,5,19,305,1976,54613,494901,19460545,226000855,11535280901,
%T A368888 163226844144,10246715573041,170910034261721,12736193619206485,
%U A368888 244588264748170651,21100437309369290497,458426839205360652760,44935948904379592796101
%N A368888 a(n) = Sum_{k=0..floor(n/2)} n^(2*k) * binomial(n-k,k).
%F A368888 a(n) = [x^n] 1/(1 - x - (n*x)^2).
%F A368888 a(n) ~ (exp(1/2) + (-1)^n*exp(-1/2)) * n^n / 2. - _Vaclav Kotesovec_, Jan 09 2024
%t A368888 Table[Hypergeometric2F1[1/2 - n/2, -n/2, -n, -4*n^2], {n, 0, 20}] (* _Vaclav Kotesovec_, Jan 09 2024 *)
%o A368888 (PARI) a(n) = sum(k=0, n\2, n^(2*k)*binomial(n-k, k));
%Y A368888 Cf. A171180, A368889.
%Y A368888 Cf. A176233, A350467.
%K A368888 nonn,easy
%O A368888 0,3
%A A368888 _Seiichi Manyama_, Jan 09 2024