Does someone know how to calculate sum $\sum_{k=1}^n \frac{1}{(n-k)!\cdot k} $? I was working something with matrices, i.e. calculating number of all cycles in Coates digraph, and got this weird expression(multiplied by $n!$) Thanks in advance.

Does someone know how to calculate sum $\sum_{k=1}^n \frac{1}{(n-k)!\cdot k} $? I was working something with matrices, i.e. calculating number of all cycles in Coates digraph, and got this weird expression(multiplied by $n!$) Thank you in advance.