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

Author

Alois P. Heinz, Jul 17 2023

Keywords

• nonn

Examples

			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.
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..707
• Wikipedia, Partition of a set

Crossrefs

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

Programs

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