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Number of multipartite partitions with odd components

Let $Q_r(a_1,\dots,a_r)$ be the number of odd partitions of the $r$-vector $(a_1,a_2,\dots,a_r)$. What is known about the sequence $Q_r(n,n,\dots,n)$, ($n=1,2,\dots$)? … Of course the first case I'm interested in is $r=2$ since it is the classical theory of partitions for $r=1$. …