Number of set partitions of [n] with alternating parity of elements.

Terms

a(0) =1a(1) =1a(2) =2a(3) =4a(4) =8a(5) =18a(6) =40a(7) =101a(8) =254a(9) =723a(10) =2064a(11) =6586a(12) =21143a(13) =74752a(14) =266078a(15) =1029983a(16) =4013425a(17) =16843526a(18) =71136112a(19) =321150717a(20) =1458636308a(21) =7038678613a(22) =34161890155a(23) =175261038904a(24) =904125989974