Set Partitions excluding singletons (sets of size one) are counted by N. Sloane and Christian G. Bower (bowerc@usa.net) in A000296 (Formerly M3423 and N1387) Sequence : 1, 0, 1, 1, 4, 11, 41, 162, 715, 3425, 17722, 98253 (with Bell[n]=a[n-1]+a[n-2] ) But, Set Partitions excluding neighbours (k excludes k+/-1 in partition) where 1 is taken to neighbour n (making it cyclic) are also counted by A000296. Anyone for a translation from one to the other? no_singletons & cyclic_neighbours_excluded {{{1, 2, 3, 4, 5}} & {{1}, {2, 4}, {3, 5}}}, {{{1, 2}, {3, 4, 5}} & {{1, 4}, {2}, {3, 5}}}, {{{1, 2, 3}, {4, 5}} & {{1, 3}, {2, 4}, {5}}}, {{{1, 4, 5}, {2, 3}} & {{1, 3}, {2, 5}, {4}}}, {{{1, 3}, {2, 4, 5}} & {{1, 4}, {2, 5}, {3}}}, {{{1, 5}, {2, 3, 4}} & {{1}, {2}, {3, 5}, {4}}}, {{{1, 2, 5}, {3, 4}} & {{1}, {2, 4}, {3}, {5}}}, {{{1, 3, 4}, {2, 5}} & {{1}, {2, 5}, {3}, {4}}}, {{{1, 4}, {2, 3, 5}} & {{1, 3}, {2}, {4}, {5}}}, {{{1, 2, 4}, {3, 5}} & {{1, 4}, {2}, {3}, {5}}}, {{{1, 3, 5}, {2, 4}} & {{1}, {2}, {3}, {4}, {5}}} Playfully yours, Wouter =============================== This email is confidential and intended solely for the use of the individual to whom it is addressed. If you are not the intended recipient, be advised that you have received this email in error and that any use, dissemination, forwarding, printing, or copying of this email is strictly prohibited. You are explicitly requested to notify the sender of this email that the intended recipient was not reached.