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%I #12 Oct 05 2018 17:24:54
%S 1,1,10,222,8824,553870,50545008,6328330344,1041597412224,
%T 218138133235680,56650689388344000,17868469522986145536,
%U 6728682216722958185472,2981868816113406609186576,1536217706761623823662025728,910442461680276910819097616000,615053979239579281793375485526016
%N a(n) = n! * [x^n] 1/(1 + n*log(1 - x)).
%F a(n) = Sum_{k=0..n} |Stirling1(n,k)|*n^k*k!.
%F a(n) ~ sqrt(2*Pi) * n^(2*n + 1/2) / exp(n - 1/2). - _Vaclav Kotesovec_, Jul 23 2018
%t Table[n! SeriesCoefficient[1/(1 + n Log[1 - x]), {x, 0, n}], {n, 0, 16}]
%t Join[{1}, Table[Sum[Abs[StirlingS1[n, k]] n^k k!, {k, n}], {n, 16}]]
%Y Cf. A007840, A088500, A094420, A242817, A317172.
%Y Main diagonal of A320079.
%K nonn
%O 0,3
%A _Ilya Gutkovskiy_, Jul 23 2018
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