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 A354323 #11 May 24 2022 08:11:58
%S A354323 1,0,1,3,11,50,273,1687,11505,86004,700445,6163751,58148547,584622766,
%T A354323 6235669629,70286727435,834288853217,10395375065096,135592878107673,
%U A354323 1846897191981835,26212412703559515,386874121137659274,5927186655133112105,94108950154465139807
%N A354323 Expansion of e.g.f. exp( x/4 * (exp(2 * x) - 1) ).
%F A354323 a(0) = 1; a(n) = Sum_{k=2..n} k * 2^(k-3) * binomial(n-1,k-1) * a(n-k).
%F A354323 a(n) = n! * Sum_{k=0..floor(n/2)} 2^(n-3*k) * Stirling2(n-k,k)/(n-k)!.
%o A354323 (PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(exp(x/4*(exp(2*x)-1))))
%o A354323 (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-1, j-1)*v[i-j+1])); v;
%o A354323 (PARI) a(n) = n!*sum(k=0, n\2, 2^(n-3*k)*stirling(n-k, k, 2)/(n-k)!);
%Y A354323 Cf. A354325.
%K A354323 nonn
%O A354323 0,4
%A A354323 _Seiichi Manyama_, May 24 2022