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%I #10 Mar 03 2022 04:31:59
%S 1,1,5,42,492,7374,134478,2887128,71281656,1988802720,61860849552,
%T 2121993490176,79566300371952,3237181141173264,142019158472311248,
%U 6682603650677875584,335698708873243355136,17930674324049810882688,1014685181110897126616448,60641642160287342580586752
%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).
%F a(n) ~ n! * 3^(n+1) * exp(3*n) / (exp(3) - 1)^(n+1). - _Vaclav Kotesovec_, Mar 03 2022
%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^25)); Vec(serlaplace(1/(1+log(1-3*x)/3))) \\ _Michel Marcus_, Mar 02 2022
%Y Cf. A007840, A032031, A087674, A227917, A255927, A352071.
%K nonn
%O 0,3
%A _Ilya Gutkovskiy_, Mar 02 2022
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