%I #4 Aug 10 2020 00:20:48
%S 1,0,-2,33,-424,495,342864,-22382913,915074432,-913039857,
%T -5455432211200,812138028148623,-75257247474017280,
%U 1984517460320303415,1155562494647499610112,-361521639388178369672625,67461150715150454861692928,-6658374003334822571921759457
%N a(n) = n! * [x^n] 1 / (exp(n*x) - x).
%F a(n) = n! * Sum_{k=0..n} (-n * (n-k+1))^k / k!.
%t Table[n! SeriesCoefficient[1/(Exp[n x] - x), {x, 0, n}], {n, 0, 17}]
%t Join[{1}, Table[n! Sum[(-n (n - k + 1))^k/k!, {k, 0, n}], {n, 1, 17}]]
%Y Cf. A089148, A134095, A302398, A336949, A336958.
%K sign
%O 0,3
%A _Ilya Gutkovskiy_, Aug 09 2020