OFFSET
0,4
LINKS
Alois P. Heinz, Table of n, a(n) for n = 0..665
Wikipedia, Partition of a set
FORMULA
EXAMPLE
a(0) = 1: (), the empty partition.
a(1) = 1: 1.
a(2) = 1: 12.
a(3) = 2: 123, 13|2.
a(4) = 3: 1234, 124|3, 14|23.
a(5) = 6: 12345, 1235|4, 125|34, 135|24, 15|234, 15|24|3.
a(6) = 13: 123456, 12346|5, 1236|45, 1246|35, 126|345, 126|35|4, 1346|25, 136|245, 136|25|4, 146|235, 16|2345, 16|235|4, 16|25|34.
a(7) = 31: 1234567, 123457|6, 12347|56, 12357|46, 1237|456, 1237|46|5, 12457|36, 1247|356, 1247|36|5, 1257|346, 127|3456, 127|346|5, 127|36|45, 13457|26, 1347|256, 1347|26|5, 1357|246, 137|2456, 137|246|5, 137|26|45, 1457|236, 147|2356, 147|236|5, 157|2346, 17|23456, 17|2346|5, 17|236|45, 147|26|35, 17|246|35, 17|26|345, 17|26|35|4.
MAPLE
b:= proc(n, m) option remember;
`if`(m<n, b(n-1, m)*m+b(n-1, m+1), 1)
end:
a:= n-> b(n, 0):
seq(a(n), n=0..31);
CROSSREFS
KEYWORD
nonn
AUTHOR
Alois P. Heinz, May 16 2023
STATUS
approved