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%I #4 Jan 28 2021 22:05:58
%S 1,1,3,5,124,-2075,91993,-4709903,312334595,-25531783799,
%T 2524083665172,-296260739274275,40667620527027177,
%U -6446882734412545043,1167717545574222779643,-239452569059443831797303,55146244227862697483251020,-14163492441645773105212592623
%N a(n) = exp(-1) * Sum_{k>=0} (k*(k - n))^n / k!.
%F a(n) = Sum_{k=0..n} binomial(n,k) * Bell(2*n-k) * (-n)^k.
%t Table[Exp[-1] Sum[(k (k - n))^n/k!, {k, 0, Infinity}], {n, 0, 17}]
%t Join[{1}, Table[Sum[Binomial[n, k] BellB[2 n - k] (-n)^k, {k, 0, n}], {n, 1, 17}]]
%Y Cf. A000110, A020556, A020557, A290219, A334243, A340822.
%K sign
%O 0,3
%A _Ilya Gutkovskiy_, Jan 22 2021
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