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 A353289 #12 Apr 10 2022 03:13:39
%S A353289 1,0,1,2,10,51,323,2354,19535,181606,1869549,21110063,259400501,
%T A353289 3445913273,49207968328,751698726580,12231484211240,211208935989003,
%U A353289 3857425360784596,74292198980174828,1504832580013205275,31980327844846620785,711498612995378484414
%N A353289 a(n) = Sum_{k=0..floor(n/2)} (n-k)^k * |Stirling1(n-k,k)|.
%F A353289 G.f.: Sum_{k>=0} x^k * Product_{j=0..k-1} (j + k * x).
%o A353289 (PARI) my(N=40, x='x+O('x^N)); Vec(sum(k=0, N, x^k*prod(j=0, k-1, j+k*x)))
%o A353289 (PARI) a(n) = sum(k=0, n\2, (n-k)^k*abs(stirling(n-k, k, 1)));
%Y A353289 Cf. A343579, A352802, A353252.
%Y A353289 Cf. A132393, A353290.
%K A353289 nonn
%O A353289 0,4
%A A353289 _Seiichi Manyama_, Apr 09 2022