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 A354326 #14 Oct 03 2023 15:26:31
%S A354326 1,0,1,6,38,280,2538,27524,341912,4754880,73322360,1244282512,
%T A354326 23048700912,462565343552,9996300546512,231444311970720,
%U A354326 5715911385442688,149988948332148736,4167328800543910272,122218355207805620480,3773036019063284645120
%N A354326 Expansion of e.g.f. 1/(1 - x/8 * (exp(4 * x) - 1)).
%F A354326 a(0) = 1; a(n) = (1/2) * Sum_{k=2..n} k * 4^(k-2) * binomial(n,k) * a(n-k).
%F A354326 a(n) = n! * Sum_{k=0..floor(n/2)} 4^(n-2*k) * k! * Stirling2(n-k,k)/(2^k * (n-k)!).
%t A354326 With[{nn=20},CoefficientList[Series[1/(1-x/8 (Exp[4x]-1)),{x,0,nn}],x] Range[0,nn]!] (* _Harvey P. Dale_, Oct 03 2023 *)
%o A354326 (PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(1/(1-x/8*(exp(4*x)-1))))
%o A354326 (PARI) a_vector(n) = my(v=vector(n+1)); v[1]=1; for(i=1, n, v[i+1]=sum(j=2, i, j*4^(j-2)*binomial(i, j)*v[i-j+1])/2); v;
%o A354326 (PARI) a(n) = n!*sum(k=0, n\2, 4^(n-2*k)*k!*stirling(n-k, k, 2)/(2^k*(n-k)!));
%Y A354326 Cf. A354324, A354325, A354328.
%K A354326 nonn
%O A354326 0,4
%A A354326 _Seiichi Manyama_, May 24 2022