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 A367972 #10 Dec 07 2023 08:27:10
%S A367972 1,3,14,82,568,4504,40016,392368,4198784,48616320,604921600,
%T A367972 8043848960,113785080832,1705669278720,27007064393728,450422751508480,
%U A367972 7893590619881472,145052304752934912,2789743827826573312,56063169473909817344
%N A367972 Expansion of e.g.f. exp(exp(2*x) - 1)/(1 - x).
%F A367972 a(0) = 1; a(n) = Sum_{k=1..n} ((k-1)! + 2^k) * binomial(n-1,k-1) * a(n-k).
%F A367972 a(n) = n! * Sum_{k=0..n} 2^k * Bell(k)/k!, where Bell() is A000110.
%o A367972 (PARI) a_vector(n) = my(v=vector(n+1)); v[1]=1; for(i=1, n, v[i+1]=sum(j=1, i, ((j-1)!+2^j)*binomial(i-1, j-1)*v[i-j+1])); v;
%Y A367972 Cf. A101053, A367971.
%Y A367972 Cf. A000110, A367973.
%K A367972 nonn
%O A367972 0,2
%A A367972 _Seiichi Manyama_, Dec 06 2023