a(n) = Sum_t t*F(n,t), where F(n,t) (see A033185) is the number of rooted forests with n (unlabeled) nodes and exactly t rooted trees.

A005197

a(n) = Sum_t t*F(n,t), where F(n,t) (see A033185) is the number of rooted forests with n (unlabeled) nodes and exactly t rooted trees.