A362944 Number of set partitions of [2n] with n circular connectors.

1, 0, 8, 61, 1339, 27497, 700526, 20738540, 701018049, 26600152925, 1118837321664, 51638294897821, 2593507095707555, 140767051300283971, 8208477680892328056, 511665532350037672814, 33945069368611365210831, 2387678179967017695888746, 177467827693197791991904437

Offset

0,3

Links

Alois P. Heinz, Table of n, a(n) for n = 0..50

Toufik Mansour and Augustine O. Munagi, Block-connected set partitions, European J. Combin., 31 (2010), 887-902.

Wikipedia, Partition of a set

Formula

a(n) = A185983(2n,n).

Example

a(2) = 8: 1|234, 134|2, 124|3, 123|4, 12|34, 14|23, 1|24|3, 13|2|4.

Maple

b:= proc(n, i, m, t) option remember; `if`(n=0, x^(t+
     `if`(i=m and m<>1, 1, 0)), add(expand(b(n-1, j,
      max(m, j), `if`(j=m+1, 0, t+`if`(j=1 and i=m
      and j<>m, 1, 0)))*`if`(j=i+1, x, 1)), j=1..m+1))
    end:
a:= n-> coeff(b(2*n, 1, 0$2), x, n):
seq(a(n), n=0..20);

Crossrefs

Cf. A185983.

Sequence in context: A361772 A327761 A080525 * A001466 A182257 A082179

Adjacent sequences: A362941 A362942 A362943 * A362945 A362946 A362947

Keyword

nonn

Author

Alois P. Heinz, May 09 2023

Status

approved