a(n) = A000045(A003622(n)).

Terms

a(0) =1a(1) =3a(2) =8a(3) =34a(4) =144a(5) =377a(6) =1597a(7) =4181a(8) =17711a(9) =75025a(10) =196418a(11) =832040a(12) =3524578a(13) =9227465a(14) =39088169a(15) =102334155a(16) =433494437a(17) =1836311903a(18) =4807526976a(19) =20365011074a(20) =53316291173a(21) =225851433717a(22) =956722026041