A361493 Expansion of e.g.f. exp(exp(x) - 1 + x^3).
1, 1, 2, 11, 39, 172, 1163, 6547, 41772, 335139, 2486215, 20078610, 186139957, 1676540257, 16077206122, 168739976555, 1763716943267, 19358116589964, 226362412711759, 2669223655597955, 32748447519013132, 421204995451111971, 5496921281576148363
Offset: 0
Programs
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PARI
my(N=30, x='x+O('x^N)); Vec(serlaplace(exp(exp(x)-1+x^3)))
Formula
a(0) = a(1) = 1, a(2) = 2; a(n) = 6 * binomial(n-1,2) * a(n-3) + Sum_{k=1..n} binomial(n-1,k-1) * a(n-k).