We show that the number of reduced Young walls of type $D_{ n+1}^{ (2)}$ with $m$ blocks is independent of $n$ and the same as the number of strict partitions of $m$. Thus the principally specialized character $\chi_n^{ \Lambda_0}(t)$ of $V(\Lambda_0)$ over $U_q(D_{ n+1}^{ (2)})$ can be interpreted as a generating function for strict partitions. Hence we obtain an infinite family of generalizations of Euler's partition identity.
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