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Expansion of e.g.f. exp(x * exp(-x * (exp(-x) - 1))).
3

%I #9 Apr 13 2023 08:29:52

%S 1,1,1,7,13,81,391,1093,18537,577,1013131,-54339,39429853,424162753,

%T -4130181873,137131757701,-1733851435439,29708533549953,

%U -337960798083053,3890007865959661,-11844138798049659,-662440203084569279,30135319297423429783

%N Expansion of e.g.f. exp(x * exp(-x * (exp(-x) - 1))).

%F a(n) = n! * Sum_{i=0..n} (-1)^(n-i) * ( 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, A362247.

%Y Cf. A347726.

%K sign

%O 0,4

%A _Seiichi Manyama_, Apr 12 2023