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 A354325 #13 Dec 02 2022 15:00:10
%S A354325 1,0,1,3,14,80,558,4522,41864,436032,5046680,64251176,892361520,
%T A354325 13426491520,217555171568,3776935252560,69942048682112,
%U A354325 1376150998836224,28669321699355520,630448829825395840,14593473117397510400,354696400190943197184,9031466708133617225984
%N A354325 Expansion of e.g.f. 1/(1 - x/4 * (exp(2 * x) - 1)).
%F A354325 a(0) = 1; a(n) = Sum_{k=2..n} k * 2^(k-3) * binomial(n,k) * a(n-k).
%F A354325 a(n) = n! * Sum_{k=0..floor(n/2)} 2^(n-3*k) * k! * Stirling2(n-k,k)/(n-k)!.
%t A354325 With[{nn=30},CoefficientList[Series[1/(1-x/4 (Exp[2x]-1)),{x,0,nn}],x] Range[0,nn]!] (* _Harvey P. Dale_, Dec 02 2022 *)
%o A354325 (PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(1/(1-x/4*(exp(2*x)-1))))
%o A354325 (PARI) a_vector(n) = my(v=vector(n+1)); v[1]=1; for(i=1, n, v[i+1]=sum(j=2, i, j*2^(j-3)*binomial(i, j)*v[i-j+1])); v;
%o A354325 (PARI) a(n) = n!*sum(k=0, n\2, 2^(n-3*k)*k!*stirling(n-k, k, 2)/(n-k)!);
%Y A354325 Cf. A354313, A354323, A354326.
%K A354325 nonn
%O A354325 0,4
%A A354325 _Seiichi Manyama_, May 24 2022