A372764 Number of partitions of [n] having exactly two blocks of minimal size.

0, 0, 1, 0, 9, 10, 70, 336, 1393, 6210, 41331, 228635, 1315974, 8779134, 61675419, 434566510, 3237964993, 25386526258, 207569429548, 1756564362651, 15418550267179, 140015129879331, 1316198207272686, 12786566843038549, 128035136707876270, 1319513338177755510

Offset

0,5

Links

Alois P. Heinz, Table of n, a(n) for n = 0..576

Wikipedia, Partition of a set

Example

a(2) = 1: 1|2.
a(4) = 9: 12|34, 12|3|4, 13|24, 13|2|4, 14|23, 1|23|4, 14|2|3, 1|24|3, 1|2|34.
a(5) = 10: 123|4|5, 124|3|5, 125|3|4, 134|2|5, 135|2|4, 1|234|5, 1|235|4, 145|2|3, 1|245|3, 1|2|345.

Maple

b:= proc(n, m, t) option remember; `if`(n=0,
     `if`(t=2, 1, 0), add(binomial(n-1, j-1)*b(n-j, min(j, m),
     `if`(j<m, 1, `if`(j=m, min(3, t+1), t))), j=1..n))
    end:
a:= n-> b(n$2, 0):
seq(a(n), n=0..25);

Crossrefs

Column k=2 of A372762.

Sequence in context: A048070 A341527 A167708 * A135332 A098325 A101242

Adjacent sequences: A372761 A372762 A372763 * A372765 A372766 A372767

Keyword

nonn

Author

Alois P. Heinz, May 12 2024

Status

approved