Partition into distinct parts

An integer partition with no repeated part. For example, the partitions into distinct parts of $5$ are $5$, $4+1$, and $3+2$. If $d(i,n)$ counts those with all parts at most $i$, separating those that omit $i$ from those that use it exactly once givesfor $i,n\ge 1$, with $d(i,0)=1$, $d(0,n)=0$ for $n>0$, and negative remaining sums counted as zero. Removing the unique part $i$ gives a bijection proving the second term; retaining the same maximum $i$ there would instead allow repetitions.