A362944 - OEIS

%I #17 May 09 2023 19:42:11

%S 1,0,8,61,1339,27497,700526,20738540,701018049,26600152925,

%T 1118837321664,51638294897821,2593507095707555,140767051300283971,

%U 8208477680892328056,511665532350037672814,33945069368611365210831,2387678179967017695888746,177467827693197791991904437

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

%H Alois P. Heinz, <a href="/A362944/b362944.txt">Table of n, a(n) for n = 0..50</a>

%H Toufik Mansour and Augustine O. Munagi, <a href="http://dx.doi.org/10.1016/j.ejc.2009.07.001">Block-connected set partitions</a>, European J. Combin., 31 (2010), 887-902.

%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Partition_of_a_set">Partition of a set</a>

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

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

%p b:= proc(n, i, m, t) option remember; `if`(n=0, x^(t+

%p      `if`(i=m and m<>1, 1, 0)), add(expand(b(n-1, j,

%p       max(m, j), `if`(j=m+1, 0, t+`if`(j=1 and i=m

%p       and j<>m, 1, 0)))*`if`(j=i+1, x, 1)), j=1..m+1))

%p     end:

%p a:= n-> coeff(b(2*n, 1, 0$2),x,n):

%p seq(a(n), n=0..20);

%Y Cf. A185983.

%K nonn

%O 0,3

%A _Alois P. Heinz_, May 09 2023