f_k \left( {n_1 ,...,n_k } \right) = p_k \left[ {q\left( {1 - p} \right)^k + q\sum\limits_{i = 1}^{k - 1} {p^i \left( {1 - p} \right)^{k - i} \left( {\sum\limits_{\scriptstyle J \subseteq \left\{ {1,...,k} \right\} \atop 
 \scriptstyle \left| J \right| = i} {\prod\limits_{j \in J} {f_1 \left( {n_j } \right)} } } \right)} + } \right.