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%I #11 Mar 14 2023 12:58:47
%S 1,1,2,11,39,172,1163,6547,41772,335139,2486215,20078610,186139957,
%T 1676540257,16077206122,168739976555,1763716943267,19358116589964,
%U 226362412711759,2669223655597955,32748447519013132,421204995451111971,5496921281576148363
%N Expansion of e.g.f. exp(exp(x) - 1 + x^3).
%F 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).
%o (PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(exp(exp(x)-1+x^3)))
%Y Cf. A355337, A361489.
%K nonn,easy
%O 0,3
%A _Seiichi Manyama_, Mar 14 2023