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 A349863 #13 Dec 03 2021 09:52:20
%S A349863 0,1,3,-6,-2,243,-2031,3796,187212,-3860139,36467311,284357502,
%T A349863 -21796446486,538332144295,-5605176351651,-182065102478856,
%U A349863 12963817679287960,-422751776737348503,5483284328996107803,327213964461103956802,-30082452646697648945898
%N A349863 Expansion of Sum_{k>=0} k^2 * x^k/(1 + k^2 * x).
%F A349863 a(n) = Sum_{k=0..n} (-k^2)^(n-k) * k^2.
%t A349863 a[n_] := Sum[If[k == n - k == 0, 1, (-k^2)^(n - k)] * k^2, {k, 0, n}]; Array[a, 21, 0] (* _Amiram Eldar_, Dec 03 2021 *)
%o A349863 (PARI) a(n, s=2, t=2) = sum(k=0, n, (-k^t)^(n-k)*k^s);
%o A349863 (PARI) my(N=40, x='x+O('x^N)); concat(0, Vec(sum(k=0, N, k^2*x^k/(1+k^2*x))))
%Y A349863 Cf. A349852.
%K A349863 sign
%O A349863 0,3
%A A349863 _Seiichi Manyama_, Dec 02 2021