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A367971
Expansion of e.g.f. exp(exp(-x) - 1)/(1 - x).
1
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
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
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Dec 06 2023
STATUS
approved