Count of All Permutations on n Objects/Sequence

Theorem
The sequence $\sequence {s_n}$ defined as:
 * $\ds s_n = n! \sum_{k \mathop = 1}^n \dfrac 1 {k!}$

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