%I #10 Apr 13 2023 08:29:47
%S 1,1,1,7,37,201,1531,12433,112729,1158769,12920311,157007841,
%T 2063354437,29052921769,436908104179,6981843029281,118083965782321,
%U 2106973566128865,39538081855597807,778216030845226561,16027517577057849181,344635879922587951321
%N Expansion of e.g.f. exp(x * exp(x * (exp(x) - 1))).
%F a(n) = n! * Sum_{i=0..n} ( Sum_{j=0..n-i} i^j * Stirling2(n-i-j,j)/(n-i-j)! )/i!.
%o (PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(exp(x*exp(x*(exp(x)-1)))))
%Y Cf. A362244, A362245, A362246.
%Y Cf. A000258, A202152.
%K nonn
%O 0,4
%A _Seiichi Manyama_, Apr 12 2023