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 A349889 #15 Nov 19 2023 10:41:19
%S A349889 1,1,15,666,59230,8775075,1948891581,605698755508,250914820143996,
%T A349889 133610836793706405,88919025666286620475,72317513878698256697166,
%U A349889 70571883548815735717843290,81383769918571603591381635271
%N A349889 a(n) = Sum_{k=0..n} (-1)^(n-k) * k^(2*n).
%F A349889 G.f.: Sum_{k>=0} (k^2 * x)^k/(1 + k^2 * x).
%F A349889 a(n) ~ 1/(1 + exp(-2)) * n^(2*n). - _Vaclav Kotesovec_, Dec 10 2021
%t A349889 Join[{1},Table[Sum[(-1)^(n-k) k^(2n),{k,0,n}],{n,20}]] (* _Harvey P. Dale_, Nov 19 2023 *)
%o A349889 (PARI) a(n) = sum(k=0, n, (-1)^(n-k)*k^(2*n));
%o A349889 (PARI) my(N=20, x='x+O('x^N)); Vec(sum(k=0, N, (k^2*x)^k/(1+k^2*x)))
%Y A349889 Cf. A120485, A249459, A349884, A349891, A349902.
%K A349889 nonn
%O A349889 0,3
%A A349889 _Seiichi Manyama_, Dec 04 2021