I know that there is a formula where even 0 is treated as significant, but is there a formula where 1 and 0 cannot be parts?

Edit:The formula that I was referencing was (Excuse the presentation) $\frac{(n-1)!}{(k-1)!(n-k)!}$ This one discards the 0, but what I was looking for one that would discard 1 as well. Also, what I'm looking for is the compositions, not the partitions.