Is there a partition formula that counts the number of partitions of n whose smallest part is k ? I know there exists a smallest part formula (Andrews) but it does not answer my question. 


Thank you



Partitions whose smallest part is k
The number of partitions of $n$ with $m$ parts $\geq k$ is $P(n-m\cdot (k-1),m)$, i.e. the number of partitions of $n-m\cdot (k-1)$ into $m$ parts. To see this it's enough to subtract $k-1$ from each part of the original partitions of $n$.


So the total number of partitions of $n$ with parts $\geq k$ is 
$$z(n,k)=\sum\_{m=1}^{[n/k]} P(n-m\cdot (k-1),m).$$


The number of partitions of $n$ with smallest part equal $k$ is $z(n,k)-z(n,k+1)$.


The function $P$ is described in <http://mathworld.wolfram.com/PartitionFunctionP.html> and <http://oeis.org/A008284> 


