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%I #13 Dec 17 2019 02:38:53
%S 0,1,1,6,24,152,1230,12646,141274,1730984,23920800,379364664,
%T 6766026168,131337466608,2713274041296,59397879195456,
%U 1386647548658496,34745321580075648,934708252265232768,26835517455387452928,815158892950448937984
%N Expansion of e.g.f. Sum_{k>=1} log(1 + log(1/(1 - x))^k) / k.
%H Vaclav Kotesovec, <a href="/A330498/b330498.txt">Table of n, a(n) for n = 0..400</a>
%H Vaclav Kotesovec, <a href="/A330498/a330498.jpg">Graph - the asymptotic ratio</a>
%F a(n) ~ n! * c / (n * (1 - exp(-1))^n), where c = 0.6931..., conjecture: c = log(2).
%t nmax = 20; CoefficientList[Series[Sum[Log[1+Log[1/(1-x)]^k]/k, {k, 1, nmax}], {x, 0, nmax}], x] * Range[0, nmax]!
%Y Cf. A003713, A330352, A330493, A330499.
%K nonn
%O 0,4
%A _Vaclav Kotesovec_, Dec 16 2019
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