A367971 - 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