A362549 Number of partitions of [n] whose blocks can be ordered such that the i-th block (except possibly the last) has at least i elements and no block j > i has an element smaller than the i-th smallest element of block i.

1, 1, 2, 4, 9, 23, 64, 187, 566, 1777, 5820, 19944, 71343, 264719, 1011292, 3953381, 15756609, 63945484, 264384828, 1115246518, 4806957739, 21189601861, 95516470253, 439777682222, 2064164172616, 9853934668051, 47736608806520, 234235866539512, 1162618720397931

Offset

0,3

Links

Alois P. Heinz, Table of n, a(n) for n = 0..888

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) = 9: 1234, 123|4, 124|3, 12|34, 134|2, 13|24, 14|23, 1|234, 1|23|4.
a(5) = 23: 12345, 1234|5, 1235|4, 123|45, 1245|3, 124|35, 125|34, 12|345, 12|34|5, 1345|2, 134|25, 135|24, 13|245, 13|24|5, 145|23, 14|235, 14|23|5, 15|234, 1|2345, 1|234|5, 15|23|4, 1|235|4, 1|23|45.
a(6) = 64: 123456, 12345|6, 12346|5, 1234|56, 12356|4, ..., 1|2356|4, 1|235|46, 16|23|45, 1|236|45, 1|23|456.

Maple

b:= proc(n, t) option remember; `if`(n<=t, 1,
      add(b(j, t+1)*binomial(n-t, j), j=0..n-t))
    end:
a:= n-> b(n, 1):
seq(a(n), n=0..30);

Crossrefs

Cf. A000110, A007476, A092920, A210540, A362635, A362637, A362893.

Sequence in context: A000083 A092668 A164039 * A014137 A377409 A245158

Adjacent sequences: A362546 A362547 A362548 * A362550 A362551 A362552

Keyword

nonn

Author

Alois P. Heinz, Apr 24 2023

Status

approved