Subfactorial[z] \[Proportional] (1/(E z)) ((-1)^z Sum[(-1)^k/z^k, {k, 0, Infinity}] + z z! + (-1)^z Sum[((-1)^k (2 + j)^k)/(z^k (1 + j)!), {k, 0, Infinity}, {j, 0, Infinity}]) /; (Abs[z] -> Infinity)

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2007-05-02