Triangle of labeled rooted trees according to the number of increasing edges.

Terms

a(0) =1a(1) =1a(2) =1a(3) =2a(4) =5a(5) =2a(6) =6a(7) =26a(8) =26a(9) =6a(10) =24a(11) =154a(12) =269a(13) =154a(14) =24a(15) =120a(16) =1044a(17) =2724a(18) =2724a(19) =1044a(20) =120a(21) =720a(22) =8028a(23) =28636a(24) =42881a(25) =28636a(26) =8028a(27) =720a(28) =5040a(29) =69264