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

%I A362944 #17 May 09 2023 19:42:11
%S A362944 1,0,8,61,1339,27497,700526,20738540,701018049,26600152925,
%T A362944 1118837321664,51638294897821,2593507095707555,140767051300283971,
%U A362944 8208477680892328056,511665532350037672814,33945069368611365210831,2387678179967017695888746,177467827693197791991904437
%N A362944 Number of set partitions of [2n] with n circular connectors.
%H A362944 Alois P. Heinz, <a href="/A362944/b362944.txt">Table of n, a(n) for n = 0..50</a>
%H A362944 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 A362944 Wikipedia, <a href="https://en.wikipedia.org/wiki/Partition_of_a_set">Partition of a set</a>
%F A362944 a(n) = A185983(2n,n).
%e A362944 a(2) = 8: 1|234, 134|2, 124|3, 123|4, 12|34, 14|23, 1|24|3, 13|2|4.
%p A362944 b:= proc(n, i, m, t) option remember; `if`(n=0, x^(t+
%p A362944      `if`(i=m and m<>1, 1, 0)), add(expand(b(n-1, j,
%p A362944       max(m, j), `if`(j=m+1, 0, t+`if`(j=1 and i=m
%p A362944       and j<>m, 1, 0)))*`if`(j=i+1, x, 1)), j=1..m+1))
%p A362944     end:
%p A362944 a:= n-> coeff(b(2*n, 1, 0$2),x,n):
%p A362944 seq(a(n), n=0..20);
%Y A362944 Cf. A185983.
%K A362944 nonn
%O A362944 0,3
%A A362944 _Alois P. Heinz_, May 09 2023