12. Let $g(n, k)$ denote the number of ways to partition an $n$-element set into $k$ subsets, each with at least 2 elements.
(1) Find the counting formula for $g(n, 2)$ $(n \geqslant 4)$.
(2) Prove: $g(n+1, k)=n g(n-1, k-1)+k g(n, k) \quad(n \geqslant 2 k \geqslant 6)$.
(3) Find $g(7,3)$.
12. (1) $2^{n-1}-n-1$.
(3) 105.