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 A353257 #12 Apr 09 2022 08:48:36
%S A353257 1,0,-1,-2,-7,-42,-341,-3452,-41835,-590452,-9511213,-172182182,
%T A353257 -3460540075,-76455710870,-1841772619273,-48043721545240,
%U A353257 -1349168210580087,-40581475067022120,-1301688751836211065,-44352720153871514858,-1599833618118922360175
%N A353257 Expansion of Sum_{k>=0} x^k * Product_{j=0..k-1} (2 * j - x).
%F A353257 a(n) = Sum_{k=0..floor(n/2)} (-1)^k * 2^(n-2*k) * |Stirling1(n-k,k)|.
%t A353257 a[n_] := Sum[(-1)^k * 2^(n - 2*k) * Abs[StirlingS1[n - k, k]], {k, 0, Floor[n/2]}]; Array[a, 20, 0] (* _Amiram Eldar_, Apr 09 2022 *)
%o A353257 (PARI) my(N=40, x='x+O('x^N)); Vec(sum(k=0, N, x^k*prod(j=0, k-1, 2*j-x)))
%o A353257 (PARI) a(n) = sum(k=0, n\2, (-1)^k*2^(n-2*k)*abs(stirling(n-k, k, 1)));
%Y A353257 Cf. A353255, A353256, A353258.
%K A353257 sign
%O A353257 0,4
%A A353257 _Seiichi Manyama_, Apr 08 2022