Count of All Permutations on n Objects/Sequence

Count of All Permutations on $n$ Objects: Sequence

The sequence $\sequence {s_n}$ defined as:

$\ds s_n = n! \sum_{k \mathop = 0}^{n - 1} \dfrac 1 {k!}$

begins:

$1, 4, 15, 64, 325, 1956, 13699, 109600, 986409, 9864100, \ldots$

This sequence is A1005726 in the On-Line Encyclopedia of Integer Sequences (N. J. A. Sloane (Ed.), 2008).