Number of 123 avoiding set partitions of [n].

Terms

a(0) =1a(1) =1a(2) =3a(3) =7a(4) =21a(5) =61a(6) =199a(7) =659a(8) =2345a(9) =8569a(10) =32971a(11) =130527a(12) =538045a(13) =2279733a(14) =9987727a(15) =44897131a(16) =207693905a(17) =983926001a(18) =4780294291a(19) =23740460215a(20) =120595843941a(21) =625175300653