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%I #7 Jun 06 2022 09:24:23
%S 1,1,-1,6,-48,534,-7542,129240,-2603736,60292512,-1577546928,
%T 46021512096,-1480976147664,52110720451152,-1990258155061776,
%U 81995762243700864,-3624527727510038784,171109526616468957312,-8591991935936929932672,457246520477143117555968
%N Expansion of e.g.f. 1 / (1 - log(1 + 3*x) / 3).
%F a(n) = Sum_{k=0..n} Stirling1(n,k) * k! * 3^(n-k).
%F a(0) = 1; a(n) = Sum_{k=1..n} binomial(n,k) * (k-1)! * (-3)^(k-1) * a(n-k).
%t nmax = 19; CoefficientList[Series[1/(1 - Log[1 + 3 x]/3), {x, 0, nmax}], x] Range[0, nmax]!
%t Table[Sum[StirlingS1[n, k] k! 3^(n - k), {k, 0, n}], {n, 0, 19}]
%o (PARI) my(x='x + O('x^20)); Vec(serlaplace(1/(1-log(1+3*x)/3))) \\ _Michel Marcus_, Jun 06 2022
%Y Cf. A006252, A087674, A255927, A335531, A352069, A354237, A354263, A354751.
%K sign
%O 0,4
%A _Ilya Gutkovskiy_, Jun 06 2022
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