A362637 Number of partitions of [n] whose blocks are ordered with increasing least elements and where block i (except possibly the last) has size at least i.

1, 1, 2, 4, 10, 30, 96, 323, 1184, 4784, 20708, 93073, 431004, 2080610, 10615276, 57291063, 322921896, 1871715144, 11065738360, 66843918825, 415837464280, 2684434034706, 18010208402784, 124877499979859, 886741484322660, 6399683149311272, 46802092819866340

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

Cf. A000110, A362549, A362635, A362639.

Sequence in context: A026119 A149834 A273958 * A149835 A149836 A003289

Adjacent sequences: A362634 A362635 A362636 * A362638 A362639 A362640

Keyword

nonn

Author

Alois P. Heinz, Apr 28 2023

Status

approved