Number of n-node rooted labeled trees with deg <= 4 at root and outdegree <= 2 elsewhere.

Terms

a(0) =1a(1) =1a(2) =2a(3) =4a(4) =8a(5) =15a(6) =32a(7) =66a(8) =142a(9) =306a(10) =672a(11) =1483a(12) =3316a(13) =7446a(14) =16859a(15) =38353a(16) =87735a(17) =201510a(18) =464801a(19) =1075744a(20) =2498053a(21) =5817576a(22) =13585231a(23) =31801732a(24) =74615404a(25) =175433624a(26) =413281276a(27) =975355639a(28) =2305763635a(29) =5459480822