%I #8 Jul 14 2020 21:40:01
%S 0,1,3,197,313840,24191662624,137300308036448256,
%T 81994640912971156525105152,6958651785463110878359050928999366656,
%U 108902755985567407887534498777329973193771818418176,395560567918154447056086270973712023435510589158871531520000000000
%N a(n) = (n!)^n * Sum_{k=1..n} (-1)^(k+1) / k^n.
%F a(n) = (n!)^n * [x^n] -polylog(n,-x) / (1 - x).
%t Table[(n!)^n Sum[(-1)^(k + 1)/k^n, {k, 1, n}], {n, 0, 10}]
%t Table[(n!)^n SeriesCoefficient[-PolyLog[n, -x]/(1 - x), {x, 0, n}], {n, 0, 10}]
%o (PARI) a(n) = (n!)^n * sum(k=1, n, (-1)^(k+1) / k^n); \\ _Michel Marcus_, Jul 14 2020
%Y Cf. A024167, A036740, A060943, A142999.
%K nonn
%O 0,3
%A _Ilya Gutkovskiy_, Jul 14 2020