AUSTRIAN-POLISH 1995 Problem 6

The Alpine Club organizes four mountain trips for its $n$ members. Let $E_1, E_2, E_3, E_4$ be the teams participating in these trips. In how many ways can these teams be formed so as to satisfy $E_1 \cap E_2 \ne\varnothing$ , $E_2 \cap E_3 \ne\varnothing$ , $E_3 \cap E_4 \ne\varnothing$ ?