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 A349884 #14 Dec 04 2021 08:54:12
%S A349884 1,1,3,12,76,961,15407,221528,3260936,80774113,2462081967,50963779604,
%T A349884 922244742292,61063845514113,2868669700179871,2019727494212912,
%U A349884 -47889136910252848,461395118866593115713,5781219348638565771423,-2108738296748190078596084
%N A349884 Expansion of Sum_{k>=0} (k * x)^k/(1 + k^2 * x).
%F A349884 a(n) = Sum_{k=0..n} (-1)^(n-k) * k^(2*n-k).
%t A349884 a[n_] := Sum[If[k == 2*n - k == 0, 1, (-1)^(n - k) * k^(2*n - k)], {k, 0, n}]; Array[a, 20, 0] (* _Amiram Eldar_, Dec 04 2021 *)
%o A349884 (PARI) a(n, t=2) = sum(k=0, n, (-k^t)^(n-k)*k^k);
%o A349884 (PARI) my(N=20, x='x+O('x^N)); Vec(sum(k=0, N, (k*x)^k/(1+k^2*x)))
%Y A349884 Cf. A120485, A349885.
%Y A349884 Cf. A349856, A349859, A349863.
%K A349884 sign
%O A349884 0,3
%A A349884 _Seiichi Manyama_, Dec 03 2021