%I #8 Feb 01 2024 08:29:46
%S 1,3,21,192,2154,28434,429213,7261788,135698268,2769463335,
%T 61186736415,1452889463034,36857766745749,993941679586098,
%U 28370018078000985,853903169641805925,27014392815958815969,895723118730738795837,31048284069527339602902
%N Expansion of e.g.f. exp( exp(3*(exp(x)-1))-1 ).
%F a(n) = Sum_{k=0..n} 3^k * Stirling2(n,k) * Bell(k) = Sum_{k=0..n} Stirling2(n,k) * A247452(k).
%o (PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(exp(exp(3*(exp(x)-1))-1)))
%Y Cf. A000258, A346417.
%Y Cf. A000110, A247452.
%K nonn
%O 0,2
%A _Seiichi Manyama_, Feb 01 2024