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%I #13 Mar 06 2022 08:41:11
%S 1,1,-5,37,-413,6421,-128285,3125557,-89781053,2969440021,
%T -111109062365,4639580153077,-213856576973693,10784605095793621,
%U -590598038062108445,34901993971832092597,-2213771863243583654333,150004882482828402563221
%N Expansion of e.g.f. (2 - exp(-3*x))^(1/3).
%F a(n) = Sum_{k=0..n} (-3)^(n-k) * (Product_{j=0..k-1} (-3*j+1)) * Stirling2(n,k).
%F a(n) ~ n! * (-1)^(n+1) * Gamma(1/3) * 3^(n - 1/2) / (Pi * 2^(2/3) * n^(4/3) * log(2)^(n - 1/3)). - _Vaclav Kotesovec_, Mar 06 2022
%t m = 17; Range[0, m]! * CoefficientList[Series[(2 - Exp[-3*x])^(1/3), {x, 0, m}], x] (* _Amiram Eldar_, Mar 05 2022 *)
%o (PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace((2-exp(-3*x))^(1/3)))
%o (PARI) a(n) = sum(k=0, n, (-3)^(n-k)*prod(j=0, k-1, -3*j+1)*stirling(n, k, 2));
%Y Cf. A352121, A352123.
%Y Cf. A352113.
%K sign
%O 0,3
%A _Seiichi Manyama_, Mar 05 2022