A361489 Expansion of e.g.f. exp(exp(x) - 1 + x^3/6).
1, 1, 2, 6, 19, 72, 313, 1472, 7612, 42679, 255515, 1632710, 11065057, 79065807, 594174922, 4679473130, 38500353667, 330172915164, 2944613004359, 27253908250340, 261328607398332, 2591724561444621, 26545170005412613, 280411070646125638
Offset: 0
Programs
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PARI
my(N=30, x='x+O('x^N)); Vec(serlaplace(exp(exp(x)-1+x^3/6)))
Formula
a(0) = a(1) = 1, a(2) = 2; a(n) = binomial(n-1,2) * a(n-3) + Sum_{k=1..n} binomial(n-1,k-1) * a(n-k).