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A341587 E.g.f.: log(1 + log(1 - x))^2 / 2.

%I A341587 #11 Feb 14 2022 09:43:42
%S A341587 1,6,40,315,2908,30989,375611,5112570,77305024,1286640410,23387713930,
%T A341587 461187042992,9808283703684,223833267479764,5456669750439788,
%U A341587 141540592345674800,3892707724320135616,113153294901088030320,3466501398608272647984,111636571036702743967104,3770483138507706753943584
%N A341587 E.g.f.: log(1 + log(1 - x))^2 / 2.
%H A341587 Seiichi Manyama, <a href="/A341587/b341587.txt">Table of n, a(n) for n = 2..418</a>
%F A341587 a(n) = Sum_{k=2..n} |Stirling1(n, k) * Stirling1(k, 2)|.
%F A341587 a(n) = Sum_{k=2..n} |Stirling1(n, k)| * (k-1)! * H(k-1), where H(k) is the k-th harmonic number.
%F A341587 a(n) = Sum_{k=1..n-1} binomial(n-1, k) * A003713(k) * A003713(n-k).
%F A341587 a(n) = A052822(n) / 2.
%F A341587 a(n) ~ sqrt(2*Pi) * log(n) * n^(n - 1/2) / (exp(1) - 1)^n * (1 + (gamma - log(exp(1) - 1))/log(n)), where gamma is the Euler-Mascheroni constant A001620. - _Vaclav Kotesovec_, Feb 15 2021
%t A341587 nmax = 22; CoefficientList[Series[Log[1 + Log[1 - x]]^2/2, {x, 0, nmax}], x] Range[0, nmax]! // Drop[#, 2] &
%t A341587 Table[Sum[Abs[StirlingS1[n, k] StirlingS1[k, 2]], {k, 2, n}], {n, 2, 22}]
%Y A341587 Cf. A000254, A000558, A003713, A008275, A039814, A052822, A302547, A302548, A341588.
%K A341587 nonn
%O A341587 2,2
%A A341587 _Ilya Gutkovskiy_, Feb 15 2021