a(n) = Sum_t t*F(n,t), where F(n,t) (see A095133) is the number of forests with n (unlabeled) nodes and exactly t trees.

A005196

a(n) = Sum_t t*F(n,t), where F(n,t) (see A095133) is the number of forests with n (unlabeled) nodes and exactly t trees.