Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).
%I #10 Dec 07 2023 08:27:06
%S 1,0,2,1,19,43,461,2350,22940,185313,1969105,20981585,255992617,
%T 3300259584,46394533498,694535043925,11123040844947,189008829494295,
%U 3402841007703469,64648146404160854,1293014652241452452,27152832827254344741,597366828915334031625
%N Expansion of e.g.f. exp(exp(-x) - 1)/(1 - x).
%F a(0) = 1; a(n) = Sum_{k=1..n} ((k-1)! + (-1)^k) * binomial(n-1,k-1) * a(n-k).
%F a(n) = n! * Sum_{k=0..n} (-1)^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)!+(-1)^j)*binomial(i-1, j-1)*v[i-j+1])); v;
%Y Cf. A101053, A367972.
%Y Cf. A000110, A087650, A186755.
%K nonn
%O 0,3
%A _Seiichi Manyama_, Dec 06 2023