Number of n-node rooted unlabeled trees with exactly 3 edges at root and otherwise out-degree <= 2.

Terms

a(0) =0a(1) =0a(2) =0a(3) =0a(4) =1a(5) =1a(6) =3a(7) =6a(8) =14a(9) =29a(10) =68a(11) =147a(12) =337a(13) =757a(14) =1734a(15) =3953a(16) =9113a(17) =20988a(18) =48645a(19) =112909a(20) =263084a(21) =614201a(22) =1438001a(23) =3373253a(24) =7930660a(25) =18679005a(26) =44075988a(27) =104173194a(28) =246604137a(29) =584620470