Some infinite sums

Does anyone know what these numbers are?

k = 1) 1.000000
k = 2) 0.281718
k = 3) 0.063436
k = 4) 0.011821
k = 5) 0.001873

They represent the sum from n=1 to infinity of n/((n+k)!)

I became curious about k>1 when I found that k=1 sums to 1.

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