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 A353894 #12 May 10 2022 11:38:32
%S A353894 1,0,0,0,6,30,105,315,2128,24948,251415,2093025,16437036,148728294,
%T A353894 1693067467,21459867975,270217289280,3338860150488,42428729660751,
%U A353894 581966068060485,8654787480759700,135253842794286930,2163416823356628147,35313421249845594075
%N A353894 Expansion of e.g.f. exp( (x * (exp(x) - 1))^2 / 4 ).
%F A353894 a(n) = n! * Sum_{k=0..floor(n/4)} (2*k)! * Stirling2(n-2*k,2*k)/(4^k * k! * (n-2*k)!).
%o A353894 (PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(exp((x*(exp(x)-1))^2/4)))
%o A353894 (PARI) a(n) = n!*sum(k=0, n\4, (2*k)!*stirling(n-2*k, 2*k, 2)/(4^k*k!*(n-2*k)!));
%Y A353894 Cf. A052506, A353895, A353896.
%Y A353894 Cf. A060311, A353883, A353891.
%K A353894 nonn
%O A353894 0,5
%A A353894 _Seiichi Manyama_, May 09 2022