|
|
A362639
|
|
Number of partitions of [n] whose blocks are ordered with increasing least elements and where block i (except possibly the last) has size i.
|
|
2
|
|
|
1, 1, 1, 1, 2, 3, 4, 15, 36, 70, 120, 756, 2800, 7920, 18900, 40040, 388080, 2106000, 8408400, 27489000, 77837760, 197520960, 2756754000, 20903929200, 113809696000, 497097881280, 1847907341280, 6062876820000, 17990209036800, 343877493960000, 3501594297801600
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,5
|
|
LINKS
|
|
|
EXAMPLE
|
a(0) = 1: (), the empty partition.
a(1) = 1: 1.
a(2) = 1: 1|2.
a(3) = 1: 1|23.
a(4) = 2: 1|23|4, 1|24|3.
a(5) = 3: 1|23|45, 1|24|35, 1|25|34.
a(6) = 4: 1|23|456, 1|24|356, 1|25|346, 1|26|345.
a(7) = 15: 1|23|456|7, 1|23|457|6, 1|23|467|5, 1|24|356|7, 1|24|357|6, 1|24|367|5, 1|25|346|7, 1|25|347|6, 1|26|345|7, 1|27|345|6, 1|26|347|5, 1|27|346|5, 1|25|367|4, 1|26|357|4, 1|27|356|4.
|
|
MAPLE
|
b:= proc(n, t) option remember; `if`(n<=t, 1,
b(n-t, t+1)*binomial(n-1, t-1))
end:
a:= n-> b(n, 1):
seq(a(n), n=0..30);
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|