A000055(n+2)-A023359(n).

Terms

a(0) =1a(1) =0a(2) =0a(3) =0a(4) =0a(5) =1a(6) =5a(7) =16a(8) =50a(9) =137a(10) =377a(11) =995a(12) =2617a(13) =6785a(14) =17630a(15) =45646a(16) =118595a(17) =308645a(18) =806617a(19) =2115455a(20) =5572438a(21) =14737430a(22) =39139779a(23) =104354064a(24) =279293860a(25) =750182992a(26) =2021884234a(27) =5466813137a(28) =14826008106a(29) =40322237818