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%I #6 Aug 06 2020 06:01:30
%S 1,1,1,10,4359,91406876,111657668637280,11436881770074767723291,
%T 137560155520600195617494951186559,
%U 260122627893213770028102613184254361777327032,99781796293430843492956500115058179262448159117567276656136
%N a(n) = (n!)^n * [x^n] exp(-Sum_{k>=1} (-x)^k / (k!)^n).
%t Table[(n!)^n SeriesCoefficient[Exp[-Sum[(-x)^k/(k!)^n, {k, 1, n}]], {x, 0, n}], {n, 0, 10}]
%t b[n_, k_] := b[n, k] = If[n == 0, 1, -Sum[(-1)^(n - j) Binomial[n, j]^k (n - j) b[j, k], {j, 0, n - 1}]/n]; a[n_] := b[n, n]; Table[a[n], {n, 0, 10}]
%Y Cf. A000587, A275044, A336209, A336210, A336439.
%K nonn
%O 0,4
%A _Ilya Gutkovskiy_, Aug 05 2020
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