Number of locally nonintersecting rooted trees with n nodes.

Terms

a(0) =1a(1) =1a(2) =2a(3) =4a(4) =8a(5) =18a(6) =40a(7) =95a(8) =227a(9) =557a(10) =1382a(11) =3485a(12) =8865a(13) =22790a(14) =59022a(15) =153972a(16) =404066a(17) =1066236a(18) =2826885a(19) =7527411a(20) =20121154