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 A353254 #13 Apr 09 2022 08:49:59
%S A353254 1,0,-2,-2,0,0,-12,-88,-608,-4664,-40032,-381200,-3993520,-45685472,
%T A353254 -566975456,-7589393568,-109019255360,-1673050977024,-27321358963904,
%U A353254 -473094230383616,-8659054324278528,-167044915214322816,-3387793305708038400,-72061754672510128384
%N A353254 Expansion of Sum_{k>=0} x^k * Product_{j=0..k-1} (j - 2 * x).
%F A353254 a(n) = Sum_{k=0..floor(n/2)} (-2)^k * |Stirling1(n-k,k)|.
%t A353254 a[n_] := Sum[(-2)^k * Abs[StirlingS1[n - k, k]], {k, 0, Floor[n/2]}]; Array[a, 25, 0] (* _Amiram Eldar_, Apr 09 2022 *)
%o A353254 (PARI) my(N=40, x='x+O('x^N)); Vec(sum(k=0, N, x^k*prod(j=0, k-1, j-2*x)))
%o A353254 (PARI) a(n) = sum(k=0, n\2, (-2)^k*abs(stirling(n-k, k, 1)));
%Y A353254 Cf. A343579, A353252, A353253.
%Y A353254 Cf. A353261.
%K A353254 sign
%O A353254 0,3
%A A353254 _Seiichi Manyama_, Apr 08 2022