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

Author

Alois P. Heinz, May 09 2023

Keywords

• nonn

Examples

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

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

Crossrefs

Cf. A185983.

Programs

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);

Formula

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