This problem is about set partitions. A set partition is a way to partition a set into several disjoint subsets. For example, there are `5` set partitions of `\{1,2,3\}`. They are `\{\{1,2,3\}\}`, `\{\{1\},\{2,3\}\}`, `\{\{2\},\{1,3\}\}`, `\{\{3\},\{1,2\}\}`, `\{\{1\},\{2\},\{3\}\}`. The number of set partitions of `\{1,2,\cdots,n\}` is counted by Bell numbers(A000110).
`a(n)` is the number of set partitions of `\{1,2,\cdots,n\}` such that each part in the set partition has almost equal sum. It means the difference between the largest sum and the smallest sum is at most `1`.
For example, `a(4)=3` because there are `3` such set partitions, `\{\{1,2,3,4\}\}`, `\{\{1,4\},\{2,3\}\}`, `\{\{1,2\},\{3\},\{4\}\}`. `a(5)=5` because there are `5` such set partitions, `\{\{1,2,3,4,5\}\}`, `\{\{1,2,4\},\{3,5\}\}`, `\{\{1,2,5\},\{3,4\}\}`, `\{\{1,3,4\},\{2,5\}\}`, `\{\{1,4\},\{2,3\},\{5\}\}`.
Find `a(n)`.