A367971 Expansion of e.g.f. exp(exp(-x) - 1)/(1 - x).

1, 0, 2, 1, 19, 43, 461, 2350, 22940, 185313, 1969105, 20981585, 255992617, 3300259584, 46394533498, 694535043925, 11123040844947, 189008829494295, 3402841007703469, 64648146404160854, 1293014652241452452, 27152832827254344741, 597366828915334031625

Offset

0,3

Links

Table of n, a(n) for n=0..22.

Formula

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

a(n) = n! * Sum_{k=0..n} (-1)^k * Bell(k)/k!, where Bell() is A000110.

Prog

(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;

Crossrefs

Cf. A101053, A367972.

Cf. A000110, A087650, A186755.

Sequence in context: A181870 A070890 A123907 * A013016 A012901 A013021

Adjacent sequences: A367968 A367969 A367970 * A367972 A367973 A367974

Keyword

nonn

Author

Seiichi Manyama, Dec 06 2023

Status

approved