Number of n-node rooted trees of height at most 3.

Terms

a(0) =1a(1) =1a(2) =1a(3) =2a(4) =4a(5) =8a(6) =15a(7) =29a(8) =53a(9) =98a(10) =177a(11) =319a(12) =565a(13) =1001a(14) =1749a(15) =3047a(16) =5264a(17) =9054a(18) =15467a(19) =26320a(20) =44532a(21) =75054a(22) =125904a(23) =210413a(24) =350215a(25) =580901a(26) =960035a(27) =1581534a(28) =2596913a(29) =4251486