a(2n) = A011900(n), a(2n+1) = A001109(n+1).

Terms

a(0) =1a(1) =1a(2) =3a(3) =6a(4) =15a(5) =35a(6) =85a(7) =204a(8) =493a(9) =1189a(10) =2871a(11) =6930a(12) =16731a(13) =40391a(14) =97513a(15) =235416a(16) =568345a(17) =1372105a(18) =3312555a(19) =7997214a(20) =19306983a(21) =46611179a(22) =112529341a(23) =271669860a(24) =655869061a(25) =1583407981a(26) =3822685023a(27) =9228778026a(28) =22280241075a(29) =53789260175