A367972 - OEIS

%I #10 Dec 07 2023 08:27:10

%S 1,3,14,82,568,4504,40016,392368,4198784,48616320,604921600,

%T 8043848960,113785080832,1705669278720,27007064393728,450422751508480,

%U 7893590619881472,145052304752934912,2789743827826573312,56063169473909817344

%N Expansion of e.g.f. exp(exp(2*x) - 1)/(1 - x).

%F a(0) = 1; a(n) = Sum_{k=1..n} ((k-1)! + 2^k) * binomial(n-1,k-1) * a(n-k).

%F a(n) = n! * Sum_{k=0..n} 2^k * Bell(k)/k!, where Bell() is A000110.

%o (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 Cf. A101053, A367971.

%Y Cf. A000110, A367973.

%K nonn

%O 0,2

%A _Seiichi Manyama_, Dec 06 2023