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%I #6 Aug 13 2020 22:42:43
%S 1,0,2,3,52,255,4146,38766,688584,9685017,195875110,3655101703,
%T 84872077500,1955205893680,51896551499898,1412668946049315,
%U 42475968202854160,1328074354724554471,44778480417250291566,1577210136570598631318
%N a(n) = exp(-n) * Sum_{k>=0} (k - n)^n * n^k / k!.
%F a(n) = n! * [x^n] exp(n*(exp(x) - 1 - x)).
%F a(n) = Sum_{k=0..n} binomial(n,k) * (-n)^(n-k) * BellPolynomial_k(n).
%t Table[n! SeriesCoefficient[Exp[n (Exp[x] - 1 - x)], {x, 0, n}], {n, 0, 19}]
%t Unprotect[Power]; 0^0 = 1; Table[Sum[Binomial[n, k] (-n)^(n - k) BellB[k, n], {k, 0, n}], {n, 0, 19}]
%Y Cf. A000296, A194689, A242817, A334242, A335867.
%K nonn
%O 0,3
%A _Ilya Gutkovskiy_, Aug 13 2020
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