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 A353252 #19 Apr 10 2022 01:55:54
%S A353252 1,0,2,2,8,24,100,488,2832,19096,147296,1281392,12422864,132870368,
%T A353252 1554525152,19750621216,270817685568,3986140113792,62686410981696,
%U A353252 1048946532137216,18608550117641728,348854564104019072,6891109834644748032,143058034748452036352
%N A353252 Expansion of Sum_{k>=0} x^k * Product_{j=0..k-1} (j + 2 * x).
%H A353252 Seiichi Manyama, <a href="/A353252/b353252.txt">Table of n, a(n) for n = 0..451</a>
%F A353252 a(n) = Sum_{k=0..floor(n/2)} 2^k * |Stirling1(n-k,k)|.
%t A353252 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 A353252 (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 A353252 (PARI) a(n) = sum(k=0, n\2, 2^k*abs(stirling(n-k, k, 1)));
%Y A353252 Cf. A352802, A343579, A353253, A353254.
%Y A353252 Cf. A097341.
%K A353252 nonn
%O A353252 0,3
%A A353252 _Seiichi Manyama_, Apr 08 2022