A360991 Expansion of e.g.f. exp(exp(x) - 1 + x^2/2).
1, 1, 3, 8, 30, 117, 533, 2599, 13919, 79620, 487810, 3167265, 21744187, 157020697, 1189321019, 9417789650, 77774264012, 668233623419, 5961395449795, 55117233908411, 527263186773227, 5210880621612366, 53130216638022540, 558176360466846439
Offset: 0
Programs
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PARI
my(N=30, x='x+O('x^N)); Vec(serlaplace(exp(exp(x)-1+x^2/2)))
Formula
a(0) = a(1) = 1; a(n) = (n-1) * a(n-2) + Sum_{k=1..n} binomial(n-1,k-1) * a(n-k).