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%I #10 Jul 16 2024 15:16:44
%S 1,2,16,206,3634,81308,2203300,70110920,2562224200,105749169920,
%T 4864704955360,246809377578080,13690337856245920,824235763862751680,
%U 53528771980276233280,3730024030461061339520,277598358023069362894720,21975673266870666302685440
%N Expansion of e.g.f. 1 / (1 + log(1 - 3*x))^(2/3).
%F a(n) = Sum_{k=0..n} 3^(n-k) * (Product_{j=0..k-1} (3*j+2)) * |Stirling1(n,k)|.
%F a(0) = 1; a(n) = Sum_{k=1..n} 3^k * (1 - 1/3 * k/n) * (k-1)! * binomial(n,k) * a(n-k).
%t With[{nn=20},CoefficientList[Series[1/(1+Log[1-3x])^(2/3),{x,0,nn}],x] Range[0,nn]!] (* _Harvey P. Dale_, Jul 16 2024 *)
%o (PARI) a(n) = sum(k=0, n, 3^(n-k)*prod(j=0, k-1, 3*j+2)*abs(stirling(n, k, 1)));
%Y Cf. A367428.
%K nonn
%O 0,2
%A _Seiichi Manyama_, Nov 18 2023
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