Ramanujan Type Congruences for a Partition Function

Abstract

We investigate the arithmetic properties of a certain function $b(n)$ given by $\sum\limits_{n=0}^\infty b(n)q^n=(q;q)_\infty^{-2}(q^2;q^2)_\infty^{-2}$. One of our main results is $b(9n+7)\equiv 0\ ({\rm mod\ }9)$.