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 A349859 #13 Dec 03 2021 09:53:11
%S A349859 0,1,1,-4,8,57,-771,4168,22504,-943255,13349105,-48905364,-3284972544,
%T A349859 117005181841,-2071095992867,-2153841382168,1791029813641424,
%U A349859 -79511121545541327,1867021096818903489,8850156160819959100,-3592582141732300745000
%N A349859 Expansion of Sum_{k>=0} k * x^k/(1 + k^2 * x).
%F A349859 a(n) = Sum_{k=0..n} (-k^2)^(n-k) * k.
%t A349859 a[n_] := Sum[If[k == n - k == 0, 1, (-k^2)^(n-k)] * k, {k, 0, n}]; Array[a, 21, 0] (* _Amiram Eldar_, Dec 03 2021 *)
%o A349859 (PARI) a(n, s=1, t=2) = sum(k=0, n, (-k^t)^(n-k)*k^s);
%o A349859 (PARI) my(N=40, x='x+O('x^N)); concat(0, Vec(sum(k=0, N, k*x^k/(1+k^2*x))))
%Y A349859 Cf. A349860, A349861.
%K A349859 sign
%O A349859 0,4
%A A349859 _Seiichi Manyama_, Dec 02 2021