A family of partitions with attached parts and `N copies of N'
The authors give the formula \[ \sum^\infty_{n=0} {q^{kn^2+(j-k)n} \over(q^j;q^k)_n (q^k;q^k)_n}= {1\over(q^j; q^k)_\infty}, \] which they observe is a special case of Heine's \(_2\varphi_1\)-summation formula, and give some combinatorial consequences for partitions. Several explicit examples are given, making the results easy to understand.
scientific article; zbMATH DE number 1506829