OFFSET
0,3
LINKS
Alois P. Heinz, Table of n, a(n) for n = 0..695
Wikipedia, Partition of a set
EXAMPLE
a(0) = 1: (), the empty partition.
a(1) = 1: 1.
a(2) = 2: 12, 1|2.
a(3) = 4: 123, 12|3, 13|2, 1|23.
a(4) = 10: 1234, 123|4, 124|3, 12|34, 134|2, 13|24, 14|23, 1|234, 1|23|4, 1|24|3.
a(5) = 30: 12345, 1234|5, 1235|4, 123|45, 1245|3, 124|35, 125|34, 12|345, 12|34|5, 12|35|4, 1345|2, 134|25, 135|24, 13|245, 13|24|5, 13|25|4, 145|23, 14|235, 14|23|5, 15|234, 1|2345, 1|234|5, 15|23|4, 1|235|4, 1|23|45, 14|25|3, 15|24|3, 1|245|3, 1|24|35, 1|25|34.
MAPLE
b:= proc(n, t) option remember; `if`(n=0, 1, `if`(n<=t, 1,
add(b(n-j, t+1)*binomial(n-1, j-1), j=t..n)))
end:
a:= n-> b(n, 1):
seq(a(n), n=0..30);
CROSSREFS
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Apr 28 2023
STATUS
approved