OFFSET
0,6
LINKS
Wikipedia, Partition of a set
FORMULA
a(7) = 6: 12|3, 134|2, 13|24, 14|23, 1|234, 123456.
a(8) = 11: 124|3, 12|34, 1345|2, 134|25, 135|24, 13|245, 145|23, 14|235, 15|234, 1|2345, 1234567.
MAPLE
b:= proc(n, i, t, m) option remember; `if`(n=0, t^(m-i+1),
`if`((i+m)*(m+1-i)/2<n or i>n, 0, `if`(t=0, 0,
t*b(n, i+1, t, m))+ b(n-i, i+1, t+1, m)))
end:
a:= n-> add(b(k, 1, 0, n-k), k=0..n):
seq(a(n), n=0..42);
CROSSREFS
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Dec 14 2023
STATUS
editing