5
Jelly, 7 6 bytes
-1 byte thanks to @Dennis (convert from unary ḅ1, rather than sum for each for each S€€)
1ẋŒṖḅ1
TryItOnline
How?
1ẋŒṖḅ1 - Main link: n e.g. 4
1ẋ - repeat 1 n times [1,1,1,1]
ŒṖ - partitions of a list [[[1],[1],[1],[1]], [[1],[1],[1,1]], [[1],[1...