In order...
231, 1, 385, 627, 30, 627, 30, 176,135
The answer is a single word. Good luck!
Partition
The diagram depicts the sequence of partitioning of boxes (integers). This led me to look at the partition function a(n)OEIS. The listed values correspond to a(n) of various n values. These n-values are between 1 and 20 and setting them to their alphabet index gives the answer.