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%I #8 Aug 14 2021 08:26:31
%S 1,1,6,72,1254,28794,819888,27869316,1101032100,49570797780,
%T 2505156062472,140417898936336,8644973807845368,579908437058338920,
%U 42098286646367326368,3288252917244250703664,274974019392668843164176,24510436934573885695407504,2319947117871178825560902112
%N E.g.f.: 1 / (1 - 6 * log(1 + x))^(1/6).
%C In general, for k > 1, if e.g.f. = 1 / (1 - k*log(1 + x))^(1/k), then a(n) ~ n! * exp(1/k^2) / (Gamma(1/k) * k^(1/k) * n^(1 - 1/k) * (exp(1/k) - 1)^(n + 1/k)). - _Vaclav Kotesovec_, Aug 14 2021
%F a(n) = Sum_{k=0..n} Stirling1(n,k) * A008542(k).
%F a(n) ~ n! * exp(1/36) / (Gamma(1/6) * 6^(1/6) * n^(5/6) * (exp(1/6) - 1)^(n + 1/6)). - _Vaclav Kotesovec_, Aug 14 2021
%t nmax = 18; CoefficientList[Series[1/(1 - 6 Log[1 + x])^(1/6), {x, 0, nmax}], x] Range[0, nmax]!
%t Table[Sum[StirlingS1[n, k] 6^k Pochhammer[1/6, k], {k, 0, n}], {n, 0, 18}]
%Y Cf. A006252, A008542, A320343, A346985, A347019, A347020, A347021, A347022.
%K nonn
%O 0,3
%A _Ilya Gutkovskiy_, Aug 11 2021
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