Number of rooted trees on n nodes with strictly thinning limbs.

Terms

a(0) =1a(1) =1a(2) =1a(3) =2a(4) =3a(5) =4a(6) =7a(7) =12a(8) =19a(9) =31a(10) =51a(11) =85a(12) =144a(13) =245a(14) =417a(15) =712a(16) =1221a(17) =2091a(18) =3600a(19) =6216a(20) =10763a(21) =18691a(22) =32546a(23) =56782a(24) =99271a(25) =173849a(26) =304877a(27) =535412a(28) =941385a(29) =1657069