a(n) = floor(bell(2n)/bell(n)^2), bell = A000110.

Terms

a(0) =1a(1) =2a(2) =3a(3) =8a(4) =18a(5) =42a(6) =102a(7) =248a(8) =611a(9) =1525a(10) =3845a(11) =9787a(12) =25118a(13) =64944a(14) =169047a(15) =442727a(16) =1165990a(17) =3086692a(18) =8210400a(19) =21936230a(20) =58851484a(21) =158502600a(22) =428446818a(23) =1162110731a(24) =3162318827a(25) =8631705612a(26) =23629386708a(27) =64865101678a(28) =178531867765a(29) =492622401009