Number of rooted trees with n nodes where the number of distinct branches under each node is <= 2.

Terms

a(0) =1a(1) =1a(2) =2a(3) =4a(4) =9a(5) =20a(6) =46a(7) =106a(8) =248a(9) =583a(10) =1393a(11) =3343a(12) =8111a(13) =19801a(14) =48719a(15) =120489a(16) =299787a(17) =749258a(18) =1881216a(19) =4741340a(20) =11993672a(21) =30436507a(22) =77471471a(23) =197726053a(24) =505917729a(25) =1297471092a(26) =3334630086a(27) =8587369072a(28) =22155278381a(29) =57259037225