Number of set partitions of [n] with alternating parity of elements and exactly three blocks.

Terms

a(0) =1a(1) =3a(2) =7a(3) =14a(4) =30a(5) =57a(6) =119a(7) =224a(8) =460a(9) =867a(10) =1761a(11) =3338a(12) =6734a(13) =12861a(14) =25843a(15) =49748a(16) =99744a(17) =193431a(18) =387365a(19) =756062a(20) =1513138a(21) =2969265a(22) =5940567a(23) =11708072a(24) =23420228a(25) =46317195a(26) =92642569a(27) =183707186a(28) =367430742a(29) =730111269