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 A349853 #19 Dec 03 2021 09:54:15
%S A349853 0,1,3,2,4,11,-13,36,56,-515,2067,-3890,-9620,129047,-664349,1837920,
%T A349853 2388704,-67004679,478198563,-1994889926,1669470804,56929813955,
%U A349853 -615188040173,3794477505596,-12028579019512,-50780206473195,1172949397924211,-10766410530764090
%N A349853 Expansion of Sum_{k>=0} k^2 * x^k/(1 + k * x).
%F A349853 a(n) = Sum_{k=0..n} (-k)^(n-k+2).
%t A349853 a[n_] := Sum[(-k)^(n - k + 2), {k, 0, n}]; Array[a, 28, 0] (* _Amiram Eldar_, Dec 02 2021 *)
%o A349853 (PARI) a(n, s=2, t=1) = sum(k=0, n, (-k^t)^(n-k)*k^s);
%o A349853 (PARI) my(N=40, x='x+O('x^N)); concat(0, Vec(sum(k=0, N, k^2*x^k/(1+k*x))))
%Y A349853 Cf. A038125, A349852, A349854, A349855.
%K A349853 sign
%O A349853 0,3
%A A349853 _Seiichi Manyama_, Dec 02 2021