From trees with valency <= 3.

Terms

a(0) =1a(1) =2a(2) =5a(3) =15a(4) =48a(5) =166a(6) =596a(7) =2221a(8) =8472a(9) =32995a(10) =130507a(11) =523100a(12) =2119454a(13) =8667529a(14) =35727261a(15) =148285069a(16) =619172847a(17) =2599212499a(18) =10963049307a(19) =46437309218a(20) =197454056586a(21) =842504023722