A364282 Number of partitions of [n] with distinct block sizes such that each block contains exactly one block size different from its own as an element.

1, 0, 0, 1, 1, 4, 11, 24, 52, 226, 969, 2281, 8960, 29898, 193202, 1075509, 3346852, 14280775, 75858992, 332978617, 2839114204, 19507400962, 75453432614, 383685116089, 2030801987312, 14025840725149, 77948290561659, 884660446815877, 7273497958681824

Offset

0,6

Links

Alois P. Heinz, Table of n, a(n) for n = 0..707

Wikipedia, Partition of a set

Example

a(3) = 1: 13|2.
a(4) = 1: 124|3.
a(5) = 4: 1235|4, 124|35, 125|34, 13|245.
a(6) = 11: 12346|5, 1235|46, 1236|45, 1256|34, 14|2356, 145|2|36, 14|256|3, 146|2|35, 15|246|3, 16|245|3, 156|2|34.

Maple

f:= proc(n) option remember; `if`(n<2, 1-n, (n-1)*(f(n-1)+f(n-2))) end:
a:= proc(m) option remember; local b; b:=
      proc(n, i, p) option remember; `if`(i*(i+1)/2<n, 0,
       `if`(n=0, p!*f(m-p), b(n, i-1, p)+b(n-i, min(n-i, i-1), p-1)/(i-1)!))
      end: b(m$3)
    end:
seq(a(n), n=0..30);

Crossrefs

Cf. A000110, A000166, A007837, A364207, A363881, A364278, A364283.

Sequence in context: A258472 A007678 A339493 * A159350 A159348 A159349

Adjacent sequences: A364279 A364280 A364281 * A364283 A364284 A364285

Keyword

nonn

Author

Alois P. Heinz, Jul 17 2023

Status

approved