A partition `\lambda` of integer `n` can be represented by a unique Young diagram. The parition `lambda` is called the shape of the Young diagram.
For example, `\lambda=(4,2,1)` is a partition of `7` then the Young diagram of shape `(4,2,1)` has `7` boxes and the bottom level has `4` boxes, the second level has `2` boxes and the third level has `1` box. In the picture, Young diagrams of shape `(4,2,1)`, `(5,3^2,2)` and `(3,1^3)` are drawn respectively.
Find `a(n)`.
Updated 04/08/2015
Typos are fixed.