%I #4 Dec 19 2019 16:47:29
%S 1,0,5,89,2737,121399,7316101,572218716,56142822849,6731180810945,
%T 965898950508901,163116461798211503,31969444766902475185,
%U 7187057932197297484108,1834860441330563739401765,527403671798720265634312349,169396494914472404237224898305
%N a(n) = exp(-1) * Sum_{k>=0} (n*k - 1)^n / k!.
%F a(n) = n! * [x^n] exp(exp(n*x) - x - 1).
%F a(n) = Sum_{k=0..n} (-1)^(n - k) * binomial(n,k) * n^k * Bell(k).
%t Table[Exp[-1] Sum[(n k - 1)^n/k!, {k, 0, Infinity}], {n, 0, 16}]
%t Join[{1}, Table[Sum[(-1)^(n - k) Binomial[n, k] n^k BellB[k], {k, 0, n}], {n, 1, 16}]]
%t Table[n! SeriesCoefficient[Exp[Exp[n x] - x - 1], {x, 0, n}], {n, 0, 16}]
%Y Cf. A000110, A000296, A124311, A292914, A307066, A330604.
%K nonn
%O 0,3
%A _Ilya Gutkovskiy_, Dec 19 2019
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