How to find formula for the given recurrence?

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Given: $f(0)=0$ , $f(1)=1$ and a constant $n$
Recurrence : $f(i)=(2^{i}-1)^{n}-^iC_1f(i-1)-^iC_2f(i-2)-^iC_3f(i-3)...-^iC_if(i-i)$
Find formula of $f(m)$ for some given $n$? ($^nC_k$ means number of ways choosing $k$ items from $n$ items)