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.

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

Offset

0,5

Links

Alois P. Heinz, Table of n, a(n) for n = 0..724

Wikipedia, Partition of a set

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

Cf. A000110, A362637.

Sequence in context: A103096 A295757 A005645 * A348628 A376584 A281586

Adjacent sequences: A362636 A362637 A362638 * A362640 A362641 A362642

Keyword

nonn

Author

Alois P. Heinz, Apr 28 2023

Status

approved