I need to apply a function to integer partitions of many integers, but only the partitions without duplicate numbers. `Select[IntegerPartitions[n], DuplicateFreeQ]` is obviously too memory-consuming because it generates all partitions with duplicates first and then selects the partitions without any duplicates; it does not work for large `n` values (even 100 doesn't work).

Take a look at this:

```
Length@IntegerPartitions[85]
(* 30167357 *)

Length@Select[IntegerPartitions[85], DuplicateFreeQ]
(* 121792 *)

```

Only a small portion of the partitions have no duplicates. Is there a way to generate duplicate-free partitions without wasting so much memory?

Edit:

The purpose of this is to find the coefficient of any $x^n$ in:
$$
\prod\_{i\geq1} {(1+a\_i x^i)}
$$

The output of `IntegerPartitions` (without duplicates) is useful because it would simply be `Plus @@ Times @@@ (parts[n] /. m_Integer :> a[m])`. `Coefficient` was very slow.