Triangle of coefficients of generating function of ternary rooted trees of height exactly n.

Terms

a(0) =1a(1) =1a(2) =1a(3) =1a(4) =1a(5) =2a(6) =4a(7) =4a(8) =5a(9) =4a(10) =4a(11) =3a(12) =2a(13) =1a(14) =1a(15) =1a(16) =3a(17) =8a(18) =15a(19) =27a(20) =43a(21) =67a(22) =97a(23) =136a(24) =183a(25) =239a(26) =300a(27) =369a(28) =432a(29) =498