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 A349854 #19 Dec 03 2021 09:54:01
%S A349854 0,1,7,12,14,49,13,8,596,-1967,4011,9764,-128878,664545,-1837695,
%T A349854 -2388448,67004968,-478198239,1994890287,-1669470404,-56929813514,
%U A349854 615188040657,-3794477505067,12028579020088,50780206473820,-1172949397923535,10766410530764819,-61183127006113196
%N A349854 Expansion of Sum_{k>=0} k^3 * x^k/(1 + k * x).
%F A349854 a(n) = -Sum_{k=0..n} (-k)^(n-k+3).
%t A349854 a[n_] := -Sum[(-k)^(n - k + 3), {k, 0, n}]; Array[a, 28, 0] (* _Amiram Eldar_, Dec 02 2021 *)
%o A349854 (PARI) a(n, s=3, t=1) = sum(k=0, n, (-k^t)^(n-k)*k^s);
%o A349854 (PARI) my(N=40, x='x+O('x^N)); concat(0, Vec(sum(k=0, N, k^3*x^k/(1+k*x))))
%Y A349854 Cf. A038125, A349852, A349853, A349855.
%K A349854 sign
%O A349854 0,3
%A A349854 _Seiichi Manyama_, Dec 02 2021