A374347 E.g.f. A(x) satisfies A(x) = A(x^3)^(1/3) * exp(3*x) with A(0)=1.
1, 3, 9, 33, 153, 783, 4329, 26757, 178929, 1385019, 13200489, 136901097, 1526386761, 18967459527, 242866024137, 3134483671437, 42179999959521, 579952188438003, 8370295687421001, 133701888662298801, 2247741025303683321, 39543420776223234303
Offset: 0
Programs
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PARI
my(N=30, x='x+O('x^N)); Vec(serlaplace(exp(3*sum(k=0, ceil(log(N+1)/log(3)), x^3^k/3^k))))
Formula
E.g.f.: exp( 3 * Sum_{k>=0} x^(3^k)/3^k ).