From the given condition, we can deduce that $C_{ n }^{ 5 }$ is the largest, hence $n=10$. Therefore, $$( \sqrt {2x}+ \frac {1}{x^{2}})^{n}$$ becomes $$( \sqrt {2x}+ \frac {1}{x^{2}})^{10}$$.

The general term formula for its expansion is $T_{r+1} = C_{ 10 }^{ r } \cdot ( \sqrt {2})^{10-r} \cdot x^{ \frac {10-5r}{2}}$.

Setting $\frac {10-5r}{2} = 0$, we find $r=2$. Thus, the constant term in the expansion is $C_{ 10 }^{ 2 } \cdot ( \sqrt {2})^{8} = 720$.

Therefore, the answer is $\boxed{720}$.

This problem involves using the properties of binomial coefficients to determine $n=10$, and then applying the general term formula of binomial expansion to find the constant term in the expansion. It primarily tests the application of the binomial theorem, properties of binomial coefficients, and the general term formula of binomial expansion, making it a basic question.